Title: Geometric inequalities in spaces of nonpositive curvature
Speaker: Mohammad Ghomi (Georgia Tech)
Date: 26 October 2022
Time: 6:30 pm
Venue: Microsoft Teams (online)
We will discuss total mean curvatures, i.e., integrals of symmetric functions of the principle curvatures, of hypersurfaces in Riemannian manifolds.
These quantities are fundamental in geometric variational problems as they appear in Steiner’s formula, Brunn-Minkowski theory, and Alexandrov-Fenchel
inequalities. We will describe a number of new inequalities for these integrals in non positively curved spaces, which are obtained via Reilly’s identities,
Chern’s formulas, and harmonic mean curvature flow. As applications we obtain several new isoperimetric inequalities, and Riemannian rigidity theorems.
This is joint work with Joel Spruck.