- Series
- Dissertation Defense
- Time
- Thursday, November 19, 2026 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 168
- Speaker
- John Stavroulakis – Georgia Institute of Technology – jstavroulakis3@gatech.edu
- Organizer
- John Stavroulakis
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