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A geometric lower bound on the (2g-2)th eigenvalue of a hyperbolic surface of genus g.

Thursday, 23 May, 2013 - 13:30
Prénom de l'orateur : 
Sugata
Nom de l'orateur : 
Mondal
Résumé : 

The existence of hyperbolic surfaces with small eigenvalues (eigenvalues less than 1/4) was originally
proved by B. Randol. P. Buser used a different method to show the existence of such surfaces in any
genus. Buser's construction showed the existence of closed hyperbolic surfaces of genus g with 2g-3
small eigenvalues. It is proved recently by Jean-Pierre Otal and Eulalio Rosas that 2g-3 indeed is the
maximal number i.e. for a genus g closed hyperbolic surface the (2g-2)th eigenvalue is strictly greater
than 1/4. In this talk we shall prove an explicit lower bound for the (2g-2)th eigenvalue for a genus g
closed hyperbolic surface depending only on the systole (or injectivity radius) of the surface.

Institution de l'orateur : 
Université de Toulouse
Thème de recherche : 
Théorie spectrale et géométrie
Salle : 
04
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