Geometric Analysis and Topology Seminar
Positive curvature implies existence of isoperimetric sets?
Speaker: Federico Glaudo, Institute for Advanced Studies (IAS)
Location: Warren Weaver Hall 512
Date: Friday, September 22, 2023, 11 a.m.
Over the past decade, a rich theory of existence for the isoperimetric problem in spaces of nonnegative curvature has been established by multiple authors.
We will briefly review this theory, with a special focus on the reasons why one may expect the isoperimetric problem to have a solution in any nonnegatively curved space: it is true for large enough volumes, it is true if the ambient is 2-dimensional, and it is true under appropriate assumptions on the ambient space at infinity.
The main topic of the talk will be the presentation of a counterexample to this "intuition": a 3-dimensional manifold of positive sectional curvature without isoperimetric sets for small volumes.
This is a joint work with G. Antonelli.