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% as revised.
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%NOTE: The cs \MajorSub appears at the beginning of each major subdivision
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1991 MATHEMATICS SUBJECT CLASSIFICATION
\MajorSub 14-XX Algebraic geometry
14-00 General reference works (handbooks, dictionaries,
bibliographies, etc.)
14-01 Instructional exposition (textbooks, tutorial papers, etc.)
14-02 Research exposition (monographs, survey articles)
14-03 Historical (must be assigned at least one classification
number from Section 01)
14-04 Explicit machine computation and programs (not the theory
of computation or programming)
14-06 Proceedings, conferences, collections, etc.
14Axx Foundations
14A05 Relevant commutative algebra, See also {13-XX}
14A10 Varieties
14A15 Schemes
14A20 Generalizations (algebraic spaces, motifs)
14A22 Noncommutative algebraic geometry; algebraic
supervarieties, See also {14M30, 32C11, 58A50}
14A25 Elementary questions
14A99 None of the above but in this section
14Bxx Local theory, See also {32Sxx}
14B05 Singularities, See also {14E15, 14H20, 32Sxx, 58C27}
14B07 Deformations of singularities, See also {14D15, 32Sxx}
14B10 Infinitesimal methods, See also {13D10}
14B12 Local deformation theory, Artin approximation, etc., See
also {13B40, 13D10}
14B15 Local cohomology, See also {13D45, 32C36}
14B20 Formal neighborhoods
14B99 None of the above but in this section
14Cxx Cycles and subschemes
14C05 Parametrization (Chow and Hilbert schemes)
14C10 Equivalence relations
14C15 Rational equivalence rings
14C17 Intersection theory
14C20 Divisors, linear systems, invertible sheaves
14C21 Pencils, nets, webs, See also {53A60}
14C22 Picard groups
14C25 Algebraic cycles
14C30 Transcendental methods, Hodge theory, See also {14D07,
32G20, 32J25, 32S35}, Hodge conjecture
14C34 Torelli problem, See also {32G20}
14C35 Applications of methods of algebraic $K$-theory, See Also {
14F05, 19Exx}
14C40 Riemann-Roch theorems, See also {19E20, 19L10}
14C99 None of the above but in this section
14Dxx Families, fibrations
14D05 Structure of families (Picard-Lefschetz, Picard-Fuchs
theory, etc.)
14D07 Variation of Hodge structures
14D10 Arithmetic ground fields (finite, local, global)
14D15 Formal methods; deformations, See also {13D10, 14B07, 16S80
32Gxx}
14D20 Algebraic moduli problems, moduli of vector bundles, {For
analytic moduli problems, See 32G13}
14D22 Fine and coarse moduli spaces
14D25 Geometric invariants, See also {14L30}
14D99 None of the above but in this section
14Exx Mappings and correspondences
14E05 Rational maps, birational correspondences
14E07 Birational automorphisms, Cremona group and
generalizations, See also {32G20}
14E09 Automorphisms, See also {14J50, 14L27}
14E10 General correspondences
14E15 Global theory of singularities, resolution, See Also {
14B05, 32S20, 32S45}
14E20 Coverings, fundamental group (mappings)
14E22 Ramification problems, See also {11S15}
14E25 Imbeddings
14E30 Minimal models
14E35 Results in dimension $\leq 3$
14E40 Local structure of maps: etale, flat, etc., See Also {
13-XX, 14F20}
14E99 None of the above but in this section
14Fxx (Co)homology theory, See also {13Dxx}
14F05 Vector bundles, sheaves, related construction, See Also {
18F20, 32Lxx, 46M20}
14F10 Differentials and other special sheaves, See also {32C38}
14F17 Vanishing theorems, See also {32L20}
14F20 Etale and other Grothendieck topologies and cohomologies
14F25 Classical real and complex cohomology
14F30 $p$-adic cohomology, crystalline cohomology
14F32 Intersection (co)homology, See also {32S60}
14F35 Homotopy theory; fundamental groups, See also {14E20,
14H30}
14F40 de Rham cohomology, See also {14C30, 32C35, 32L10}
14F45 Topological properties
14F99 None of the above but in this section
14Gxx Arithmetic problems. Diophantine geometry, See also {11Dxx,
11Gxx}
14G05 Rationality questions, rational points
14G10 Zeta-functions and related questions, See also {11G40}
(Birch-Swinnerton-Dyer conjecture)
14G15 Finite ground fields
14G20 $p$-adic ground fields
14G25 Global ground fields
14G27 Nonalgebraically closed ground fields
14G35 Modular and Shimura varieties, See also {11F41, 11F46,
11G18}
14G40 Arithmetic varieties and schemes; Arakelov theory
14G99 None of the above but in this section
14Hxx Curves
14H05 Algebraic functions; function fields, See also {11R58}
14H10 Families, moduli (algebraic)
14H15 Families, moduli (analytic), See also {30F10, 32Gxx}
14H20 Singularities, local rings, See also {13Hxx}
14H25 Arithmetic ground fields, See also {11Dxx, 11G05, 14Gxx}
14H30 Coverings, fundamental group, See also {14E20, 14F35}
14H35 Correspondences, See also {14Exx}
14H40 Jacobians, See also {32G20}
14H42 Theta functions; Schottky problem, See also {14K25, 32G20}
14H45 Special curves and curves of low genus
14H50 Space curves
14H52 Elliptic curves, See also {11G05, 11G07, 14Kxx}
14H55 Riemann surfaces; Weierstrass points; gap sequences, See
also {30Fxx}
14H60 Vector bundles on curves, See also {14F05}
14H99 None of the above but in this section
14Jxx Surfaces and higher-dimensional varieties, {For analytic
theory, See 32Jxx}
14J05 Picard group, See also {14C22, 19A49, 32L05}
14J10 Families, moduli, classification: algebraic theory
14J15 Moduli, classification: analytic theory, See also {32G13,
32J15}
14J17 Singularities of surfaces
14J20 Arithmetic ground fields, See also {11Dxx, 11G25, 11G35,
14Gxx}
14J25 Special surfaces, {For Hilbert modular surfaces, See 14G35}
14J26 Rational and ruled surfaces
14J27 Elliptic surfaces
14J28 $K3$ surfaces and Enriques surfaces
14J29 Surfaces of general type
14J30 Special $3$-folds, See also {14E05}
14J35 Special $4$-folds, See also {14E05}
14J40 Special $n$-folds
14J45 Fano varieties
14J50 Automorphisms of surfaces and higher-dimensional varieties,
See also {14E09}
14J60 Vector bundles on surfaces and higher-dimensional
varieties, See also {14F05, 32Lxx}
14J70 Hypersurfaces
14J99 None of the above but in this section
14Kxx Abelian varieties and schemes
14K02 Isogeny
14K05 Algebraic theory
14K10 Algebraic moduli, classification
14K15 Arithmetic ground fields, See also {11Dxx, 11Fxx, 11Gxx,
14Gxx}
14K20 Analytic theory; abelian integrals and differentials
14K22 Complex multiplication, See also {11G15}
14K25 Theta functions
14K30 Picard schemes, higher Jacobians, See also {14H40, 32G20}
14K99 None of the above but in this section
14Lxx Group schemes, {For linear algebraic groups, See 20Gxx. For
Lie algebras, See 17B45}
14L05 Formal groups, $p$-divisible groups, See also {55N22}
14L10 Group varieties
14L15 Group schemes
14L17 Affine algebraic groups, hyperalgebra constructions, See
also {17B45, 18D35}
14L27 Automorphism groups, See also {14E09}
14L30 Group actions on varieties or schemes (quotients), See
also {14D25}
14L35 Classical groups (geometric aspects), See also {20Gxx,
51N30}
14L40 Other algebraic groups (geometric aspects)
14L99 None of the above but in this section
14Mxx Special varieties
14M05 Varieties defined by ring conditions (factorial,
Cohen-Macaulay, seminormal), See also {13C14, 13F45,
13H10}
14M06 Linkage, See also {13C40}
14M07 Low codimension problems, See also {14Cxx}
14M10 Complete intersections, See also {13C40}
14M12 Determinantal varieties, See also {13C40}
14M15 Grassmannians, Schubert varieties, flag manifolds, See
also {32M10, 51M35}
14M17 Homogeneous spaces and generalizations, See also {32M10,
53C30, 57T15}
14M20 Rational varieties
14M25 Toric varieties, Newton polyhedra
14M30 Supervarieties, See also {14A22, 32C11, 58A50}
14M99 None of the above but in this section
14Nxx Classical methods and problems, See also {51-XX}
14N05 Projective techniques, See also {51N35}
14N10 Enumerative problems (combinatorial problems)
14N99 None of the above but in this section
14Pxx Real algebraic and real analytic geometry
14P05 Real algebraic sets, See also {12Dxx}
14P10 Semialgebraic sets and related spaces
14P15 Real analytic and semianalytic sets, See also {32B20,
32C05}
14P20 Nash functions and manifolds, See also {32C07, 58A07}
14P25 Topology of real algebraic varieties
14P99 None of the above but in this section
14Qxx Computational aspects in algebraic geometry, See also {12-04,
68Q40}
14Q05 Curves
14Q10 Surfaces, hypersurfaces
14Q15 Higher-dimensional varieties
14Q20 Effectivity
14Q99 None of the above but in this section
\MajorSub 32-XX Several complex variables and analytic spaces, {For
infinite-dimensional holomorphy, See also 46G20, 58B12}
32-00 General reference works (handbooks, dictionaries,
bibliographies, etc.)
32-01 Instructional exposition (textbooks, tutorial papers, etc.)
32-02 Research exposition (monographs, survey articles)
32-03 Historical (must be assigned at least one classification
number from Section 01)
32-04 Explicit machine computation and programs (not the theory
of computation or programming)
32-06 Proceedings, conferences, collections, etc.
32Axx Holomorphic functions of several complex variables
32A05 Power series, series of functions
32A07 Special domains (Reinhardt, Hartogs, tube domains, etc.)
32A10 Holomorphic functions
32A15 Entire functions
32A17 Special families of functions (e.g. normal families)
32A20 Meromorphic functions
32A22 Nevanlinna theory (local); growth estimates; other
inequalities, {For geometric theory, See 32H25, 32H30}
32A25 Integral representation
32A27 Local theory of residues, See also {32C30}
32A30 Other generalizations of function theory of one complex
variable (should also be assigned at least one
classification number from Section 30), {For functions
of several hypercomplex variables, See 30G35}
32A35 ${H}^p$-spaces, See also {32M15, 42B30, 43A85, 46J15}
32A37 Other spaces of holomorphic functions (e.g. bounded mean
oscillation (BMOA), vanishing mean oscillation (VMOA)
in $n$ dimensions), See also {46Exx}
32A40 Boundary behavior
32A45 Hyperfunctions, See also {46F15}
32A99 None of the above but in this section
32Bxx Local analytic geometry, See also {13-XX and 14-XX}
32B05 Analytic algebras and generalizations, preparation theorems
32B10 Germs of analytic sets
32B15 Analytic subsets of affine space
32B20 Semi-analytic sets and subanalytic sets, See also {14P15}
32B25 Triangulation and related questions
32B99 None of the above but in this section
32Cxx General theory of analytic spaces
32C05 Real-analytic manifolds, real-analytic spaces, See Also
{14Pxx, 58A07}
32C07 Real-analytic sets, complex Nash functions, See Also
{14P15, 14P20}
32C10 Complex manifolds, {For almost complex manifolds, See
53C15}
32C11 Complex supergeometry, See also {14A22, 14M30, 58A50}
32C15 Complex spaces
32C16 CR-manifolds
32C17 Kahler geometry, {For differential-geometric methods, See
53C55}
32C18 Topology of analytic spaces
32C20 Normal analytic spaces
32C25 Analytic subsets and submanifolds
32C30 Integration on analytic sets and spaces, currents, {For
local theory, See 32A25 or 32A27}
32C35 Analytic sheaves and cohomology groups, See also {14Fxx,
18F20, 55N30}
32C36 Local cohomology of analytic spaces
32C37 Duality theorems
32C38 Sheaves of differential operators and their modules, See
also {14F10, 16S32, 35A27, 58G07}
32C81 Applications to physics
32C99 None of the above but in this section
32Dxx Analytic continuation
32D05 Domains of holomorphy
32D10 Envelopes of holomorphy
32D15 Continuation of analytic objects
32D20 Removable singularities
32D99 None of the above but in this section
32Exx Holomorphic convexity
32E05 Holomorphically convex complex spaces, reduction theory
32E10 Stein spaces, Stein manifolds
32E20 Polynomial convexity
32E25 Algebras of holomorphic functions, See also {30H05, 46J10,
46J15}
32E30 Holomorphic and polynomial approximation, Runge pairs,
interpolation
32E35 Global boundary behavior of holomorphic functions
32E99 None of the above but in this section
32Fxx Geometric convexity, partial differential operators
32F05 Plurisubharmonic functions and generalizations, See Also {
31C10}
32F07 Complex Monge-Ampere operator
32F10 $q$-convexity, $q$-concavity
32F15 Pseudoconvex domains
32F20 $\overline\partial$- and $\overline\partial_b$-Neumann
problems, See also {35N15}
32F25 Real submanifolds in complex manifolds
32F30 Pseudoconvex manifolds
32F40 CR structures, (tangential) CR operators and
generalizations
32F99 None of the above but in this section
32Gxx Deformations of analytic structures
32G05 Deformations of complex structures, See also {13D10, 16S80,
58H10, 58H15}
32G07 Deformations of special (e.g. CR) structures
32G08 Deformations of fiber bundles
32G10 Deformations of submanifolds and subspaces
32G13 Analytic moduli problems, {For algebraic moduli problems,
See 14D20, 14D22, 14H10, 14J10}, See also {14H15,
14J15}
32G15 Moduli of Riemann surfaces, Teichmuller theory, See Also {
14H15, 30Fxx}
32G20 Period matrices, variation of Hodge structure;
degenerations, See also {14D05, 14D07, 14K30}
32G34 Moduli and deformations for ordinary differential
equations, See also {34A20}
32G81 Applications to physics
32G99 None of the above but in this section
32Hxx Holomorphic mappings and correspondences
32H02 Holomorphic mappings, (holomorphic) embeddings and related
questions
32H04 Meromorphic mappings
32H10 Bergman kernel function, representative domains
32H15 Invariant metrics and pseudodistances
32H20 Hyperbolic complex manifolds
32H25 Picard-type theorems and generalizations, {For
function-theoretic properties, See 32A22}
32H30 Value distribution theory in higher dimensions, {For
function-theoretic properties, See 32A22}
32H35 Proper mappings, finiteness theorems
32H40 Boundary regularity of holomorphic maps
32H50 Iteration problems
32H99 None of the above but in this section
32Jxx Compact analytic spaces, {For Riemann surfaces, See 14Hxx,
30Fxx; for algebraic theory, See 14Jxx}
32J05 Compactification of analytic spaces
32J10 Algebraic dependence theorems
32J15 Compact surfaces
32J17 Compact $3$-folds
32J18 Compact $n$-folds $(n \ge 4)$
32J20 Algebraicity criteria
32J25 Transcendental methods of algebraic geometry, See Also {
14C30}
32J27 Compact Kahler manifolds: generalizations, classification
32J81 Applications to physics
32J99 None of the above but in this section
32Kxx Generalizations of analytic spaces {(should also be assigned
at least one other classification number in this
section)}
32K05 Banach analytic spaces, See also {58Bxx}
32K07 Formal and graded complex spaces, See also {58C50}
32K15 Differentiable functions on analytic spaces, differentiable
spaces, See also {58C25}
32K99 None of the above but in this section
32Lxx Holomorphic fiber spaces, See also {55Rxx}
32L05 Holomorphic fiber bundles and generalizations
32L07 Hermite-Einstein bundles; Kahler-Einstein bundles, See
also {53C07}
32L10 Sheaves and cohomology of sections of holomorphic vector
bundles, general results, See also {14F05, 18F20,
55N30}
32L15 Bundle convexity, See also {32F10}
32L20 Vanishing theorems
32L25 Twistor theory, double fibrations
32L30 Holomorphic foliations, See also {58F18}
32L81 Applications to physics
32L99 None of the above but in this section
32Mxx Complex spaces with a group of automorphisms
32M05 Complex Lie groups, automorphism groups of complex spaces,
See also {22E10}
32M10 Homogeneous complex manifolds, See also {14M17, 57T15}
32M12 Almost homogeneous manifolds and spaces, See also {14M17}
32M15 Hermitian symmetric spaces, bounded symmetric domains, See
also {22E10, 22E40, 53C35, 57T15}
32M99 None of the above but in this section
32Nxx Automorphic functions, See also {11Fxx, 20H10, 22E40, 30F35}
32N05 General theory of automorphic functions of several complex
variables
32N10 Automorphic forms
32N15 Automorphic functions in symmetric domains
32N99 None of the above but in this section
32P05 Non-Archimedean complex analysis (should also be assigned at
least one other classification number from Section $32$
describing the type of problem)
32Sxx Singularities
32S05 Local singularities, See also {14B05}
32S10 Invariants of analytic local rings
32S15 Equisingularity (topological and analytic), See Also {
14E15}
32S20 Global theory of singularities; cohomological properties,
See also {14E15}
32S25 (Hyper-) surface singularities, See also {14J17}
32S30 Deformations of singularities; vanishing cycles, See Also {
14B07}
32S35 Mixed Hodge theory of singular varieties, See also {14C30,
14D07}
32S40 Monodromy; relations with differential equations and
$D$-modules
32S45 Modifications; resolution of singularities, See Also {
14E15}
32S50 Topological aspects: Lefschetz theorems, topological
classification, invariants
32S55 Milnor fibration; relations with knot theory, See Also {
57M25, 57Q45}
32S60 Stratifications; constructible sheaves; intersection
cohomology, See also {58C27}
32S65 Singularities of holomorphic vector fields
32S70 Other operations on singularities
\MajorSub 53-XX Differential geometry, {For differential topology, See
57Rxx. For foundational questions of differentiable
manifolds, See 58Axx}
53-00 General reference works (handbooks, dictionaries,
bibliographies, etc.)
53-01 Instructional exposition (textbooks, tutorial papers, etc.)
53-02 Research exposition (monographs, survey articles)
53-03 Historical (must be assigned at least one classification
number from Section 01)
53-04 Explicit machine computation and programs (not the theory
of computation or programming)
53-06 Proceedings, conferences, collections, etc.
53Axx Classical differential geometry
53A04 Curves in Euclidean space
53A05 Surfaces in Euclidean space
53A07 Higher-dimension and -codimension surfaces in Euclidean
$n$-space
53A10 Minimal surfaces, surfaces with prescribed mean curvature,
See also {49Q05, 49Q10, 53C42}
53A15 Affine differential geometry
53A17 Kinematics
53A20 Projective differential geometry
53A25 Differential line geometry
53A30 Conformal differential geometry
53A35 Non-Euclidean differential geometry
53A40 Other special differential geometries
53A45 Vector and tensor analysis
53A50 Spinor analysis
53A55 Differential invariants (local theory), geometric objects
53A60 Geometry of webs, See also {14C21, 20N05}
53A99 None of the above but in this section
53Bxx Local differential geometry
53B05 Linear and affine connections
53B10 Projective connections
53B15 Other connections
53B20 Local Riemannian geometry
53B21 Methods of Riemannian geometry
53B25 Local submanifolds, See also {53C40}
53B30 Lorentz metrics, indefinite metrics
53B35 Hermitian and Kahlerian structures, See also {32Cxx}
53B40 Finsler spaces and generalizations (areal metrics)
53B50 Applications to physics
53B99 None of the above but in this section
53Cxx Global differential geometry, See also {51H25, 58-XX; for
related bundle theory, See 55Rxx, 57Rxx}
53C05 Connections, general theory
53C07 Special connections and metrics on vector bundles
(Hermite-Einstein-Yang-Mills), See also {32L07}
53C10 $G$-structures
53C12 Foliations (differential geometric aspects), See Also {
57R30, 57R32}
53C15 General geometric structures on manifolds (almost complex,
contact, symplectic, almost product structures, etc.)
53C20 Global Riemannian geometry, including pinching, See Also {
31C12, 58B20}
53C21 Methods of Riemannian geometry, including PDE methods;
curvature restrictions, See also {58G30}
53C22 Geodesics, See also {58E10}
53C23 Global topological methods (a la Gromov)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C30 Homogeneous manifolds, See also {14M15, 14M17, 32M10,
57T15}
53C35 Symmetric spaces, See also {32M15, 57T15}
53C40 Global submanifolds, See also {53B25}
53C42 Immersions (minimal, prescribed curvature, tight, etc.),
See also {49Q05, 49Q10, 53A10, 57R40, 57R42}
53C45 Global surface theory (convex surfaces a la A. D.
Aleksandrov)
53C50 Lorentz manifolds, manifolds with indefinite metrics
53C55 Hermitian and Kahlerian manifolds, See also {32Cxx}
53C56 Other complex differential geometry, See also {32Cxx}
53C60 Finsler spaces and generalizations (areal metrics), See
also {58B20}
53C65 Integral geometry, See also {52A22, 60D05}; differential
forms, currents, etc. See mainly{58Axx}
53C70 Direct methods ($G$-spaces of Busemann, etc.)
53C75 Geometric orders, order geometry, See also {51Lxx}
53C80 Applications to physics
53C99 None of the above but in this section
\MajorSub 58-XX Global analysis, analysis on manifolds, See also {{
32-XX} {32Cxx, 32Fxx}, 46-XX, 47Hxx, 53Cxx; for
geometric integration theory, See {49Fxx} {49Q15}}
58-00 General reference works (handbooks, dictionaries,
bibliographies, etc.)
58-01 Instructional exposition (textbooks, tutorial papers, etc.)
58-02 Research exposition (monographs, survey articles)
58-03 Historical (must be assigned at least one classification
number from Section 01)
58-04 Explicit machine computation and programs (not the theory
of computation or programming)
58-06 Proceedings, conferences, collections, etc.
58Axx General theory of differentiable manifolds
58A03 Topos-theoretic approach to differentiable manifolds
58A05 Differentiable manifolds, foundations
58A07 Real-analytic and Nash manifolds, See also {14P20, 32C07}
58A10 Differential forms
58A12 de Rham theory, See also {14Fxx}
58A14 Hodge theory, See also {14C30, 14Fxx, 32J25, 32S35}
58A15 Exterior differential systems (Cartan theory)
58A17 Pfaffian systems
58A20 Jets
58A25 Currents, See also {32C30, 53C65}
58A30 Vector distributions (subbundles of the tangent bundles)
58A35 Stratified sets, See also {32S60, 58C27}
58A40 Differential spaces
58A50 Supermanifolds and graded manifolds, See also {14A22,
32C11}
58A99 None of the above but in this section
58Bxx Infinite-dimensional manifolds
58B05 Homotopy and topological questions
58B10 Differentiability questions
58B12 Questions of holomorphy, See also {32-XX, 46G20}
58B15 Fredholm structures, See also {47A53}
58B20 Riemannian, Finsler and other geometric structures, See
also {53C20, 53C60}
58B25 Group structures and generalizations on
infinite-dimensional manifolds, See also {22E65, 58D05}
58B30 Noncommutative differential geometry and topology, See
also {46L30, 46L87, 46L89}
58B99 None of the above but in this section
58Cxx Calculus on manifolds; nonlinear operators, See also {47Hxx}
58C05 Real-valued functions
58C06 Set valued and function-space valued mappings, See Also {
47H04, 54C60}
58C07 Continuity properties of mappings
58C10 Holomorphic maps, See also {32-XX}
58C15 Implicit function theorems; global Newton methods
58C20 Differentiation theory (Gateaux, Frechet, etc.), See
also {26Exx, 46G05}
58C25 Differentiable maps
58C27 Singularities of differentiable maps, See also {14B05,
14E15, 32Sxx}
58C28 Catastrophes, See also {57R70, 58Exx}
58C30 Fixed point theorems on manifoldsSee also {47H10}
58C35 Integration on manifolds; measures on manifolds, See Also {
28Cxx}
58C40 Spectral theory; eigenvalue problems, See also {47H12,
58E07}
58C50 Analysis on supermanifolds or graded manifolds
58C99 None of the above but in this section
58Dxx Spaces and manifolds of mappings {(including nonlinear
versions of 46Exx)}
58D05 Groups of diffeomorphisms and homeomorphisms as manifolds,
See also {22E65, 57S05}
58D07 Groups and semigroups of nonlinear operators, See Also {
17B65, 47D03, 47D06, 47H20}
58D10 Spaces of imbeddings and immersions
58D15 Manifolds of mappings, See also {54C35}
58D17 Manifolds of metrics (esp. Riemannian)
58D19 Group actions and symmetry properties
58D20 Measures (Gaussian, cylindrical, etc.) on manifolds of maps
See{28Cxx}
58D25 Equations in function spaces; evolution equations, See
also {34Gxx, 35K22, 35R15, 47H15}
58D27 Moduli problems for differential geometric structures
58D29 Moduli problems for topological structures
58D30 Applications (in quantum mechanics (Feynman path
integrals), relativity, fluid dynamics, etc.)
58D99 None of the above but in this section
58Exx Variational problems in infinite-dimensional spaces
58E05 Abstract critical point theory (Morse theory,
Ljusternik-Schnirelman (Lyusternik-Shnirelman)
theory, etc.)
58E07 Abstract bifurcation theory
58E09 Group-invariant bifurcation theory
58E10 Applications to the theory of geodesics (problems in one
independent variable)
58E11 Critical metrics
58E12 Applications to minimal surfaces (problems in two
independent variables)
58E15 Application to extremal problems in several variables;
Yang-Mills functionals, See also {81T13}, etc.
58E17 Pareto optimality, etc., applications to economics
58E20 Harmonic maps
58E25 Applications to control theory (optimal and nonoptimal)
58E30 Variational principles
58E35 Variational inequalities (global problems)
58E40 Group actions
58E50 Applications
58E99 None of the above but in this section
58Fxx Ordinary differential equations on manifolds; dynamical
systems, See also {28D10, 34Cxx, {34Cxx} {54H20}}
58F03 One-dimensional dynamics, general symbolic dynamics, See
also {26A18}
58F05 Hamiltonian and Lagrangian systems; symplectic geometry,
See also {70Hxx, 81S10}
58F06 Geometric quantization (applications of representation
theory), See also {22E45, 81S10}
58F07 Completely integrable systems (including systems with an
infinite number of degrees of freedom)
58F08 Point-mapping properties, iterations, completeness;
dynamics of cellular automata, See also {26A18, 30D05}
58F09 Morse-Smale systems
58F10 Stability theory
58F11 Ergodic theory; invariant measures, See also {28Dxx}
58F12 Structure of attractors (and repellors)
58F13 Strange attractors; chaos and other pathologies, See Also {
70K50}
58F14 Bifurcation theory and singularities
58F15 Hyperbolic structures (expanding maps, Anosov systems,
etc.)
58F17 Geodesic and horocycle flows
58F18 Relations with foliations
58F19 Eigenvalue and spectral problems
58F20 Periodic points and zeta functions
58F21 Limit cycles, singular points, etc.
58F22 Periodic solutions
58F23 Holomorphic dynamics, See also {30D05}
58F25 Flows
58F27 Quasiperiodic flows
58F30 Perturbations
58F32 Functional-differential equations on manifolds
58F35 Invariance properties
58F36 Normal forms
58F37 Correspondences and other transformation methods (e.g.
Lie-Backlund)
58F39 Dynamical systems treatment of PDE (should be assigned
another number from 58F), See also {35B32, 35K57}
58F40 Applications
58F99 None of the above but in this section
58Gxx Partial differential equations on manifolds; differential
operators, See also {35-XX}
58G03 Elliptic equations on manifolds, general theory
58G05 Differential complexes, See also {35Nxx}; elliptic
complexes
58G07 Relations with hyperfunctions
58G10 Index theory and related fixed point theorems, See Also {
19K56, 46L80}
58G11 Heat and other parabolic equation methods
58G12 Exotic index theories, See also {19K56, 46L05, 46L10,
46L80, 46M20}
58G15 Pseudodifferential and Fourier integral operators on
manifolds, See also {35Sxx}
58G16 Hyperbolic equations
58G17 Propagation of singularities; initial value problems
58G18 Perturbations; asymptotics
58G20 Boundary value problems on manifolds
58G25 Spectral problems; spectral geometry; scattering theory,
See also {35Pxx}
58G26 Determinants and determinant bundles
58G28 Bifurcations, See also {35B32}
58G30 Relations with special manifold structures (Riemannian,
Finsler, etc.)
58G32 Diffusion processes and stochastic analysis on manifolds
58G35 Invariance and symmetry properties, See also {35A30}
58G37 Correspondences and other transformation methods (e.g.
Lie-Backlund), See also {35A22}
58G40 Applications
58G99 None of the above but in this section
58Hxx Pseudogroups, differentiable groupoids and general structures
on manifolds
58H05 Pseudogroups and differentiable groupoids, See also {22A22,
22E65}
58H10 Cohomology of classifying spaces for pseudogroup structures
(Spencer, Gelfand-Fuks, etc.), See also {57R32}
58H15 Deformations of structures, See also {32Gxx, 58G05}
58H99 None of the above but in this section
58Z05 Applications to physics