Date: Thursday, November 19th

Time:  11:00 am

Room: Skiles 168

Title: On the bow lemma and higher dimensional analogs.

Committee: Igor Belegradek, Elena Braverman (University of Calgary), Mohammad Ghomi (advisor), Galyna Livshyts, Andrzej Swiech, Erik Verriest (ECE).

Abstract:

We discuss the bow lemma or Schur comparison theorem, and in particular its higher dimensional analogs. We first investigate isoperimetry under upper and lower curvature bounds, including the Cartan-Hadamard conjecture. We then discuss Fenchel's theorem for CAT(0) spaces and its higher dimensional versions concerning tight (hyper)surfaces in Cartan-Hadamard manifolds. We also develop a rigidity mechanism for flat hypersurfaces in Alexandrov ambient spaces, which is applied to completely characterize surfaces which optimize total Gauss curvature in 3-folds with upper or lower curvature bounds.

Teams link: https://teams.microsoft.com/meet/2172100941812051?p=0YimD0FGzxQfer6TrD