CR-foliations and Morera type theorems for manifolds with attached analytic discs.

A characterization of analytic and CR functions on manifolds in C^n
is obtained in terms of analytic extensions into parametric
families of analytic discs glued up to the manifolds by their boundaries.
In particular, we answer, in smooth category, two old open questions:
on testing analyticity on smooth families of Jordan planar curves (the strip-problem) and on characterization of boundary values of holomorphic functions in C^n by analytic extendibility into a
manifold of complex lines (Globevnik-Stout conjecture).
The problems appeared of rather topological nature and are solved
by reducing to a problem of extendibility of boundary degeneracy of
CR-foliations.