Calculus of Variations and Geometric Measure Theory
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Morse index and Betti numbers of minimal hypersurfaces

Lucas Ambrozio

created by malchiodi on 06 May 2016

12 may 2016 -- 11:00   [open in google calendar]

Scuola Normale Superiore, Aula Fermi

Abstract.

As critical points of the area functional, minimal hypersurfaces of Riemannian manifolds have a well-defined Morse index. In many situations, the knowledge of the index can be used to derive conclusions about the geometry and topology of the hypersurface itself. In this talk, we will show that under certain conditions on the ambient manifold, the index of its minimal hypersurfaces grows linearly with their first Betti numbers. The hypothesis on the ambient manifold are flexible enough to include all compact symmetric spaces of rank one and small graphical perturbations of the round sphere, for example. This is a joint work with A. Carlotto and B. Sharp.

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