- Series
- Analysis Seminar
- Time
- Wednesday, January 24, 2024 - 2:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Federico Glaudo – Princeton University – fglaudo@ias.edu – https://glaudo.github.io/
- Organizer
- Galyna Livshyts
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.