Isoperimetry, Sobolev, Mass transport and Stability
Debabrata Karmakar
| Speaker |
Debabrata Karmakar
|
|---|---|
| When |
Mar 07, 2025
from 04:00 PM to 05:00 PM |
| Where | LH-111, First Floor |
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PIZZA TALK
Abstract: Starting from Gromov’s striking proof of the anisotropic isoperimetric inequality and Erausquin-Nazaret-Villani’s duality-based proof of the anisotropic Sobolev inequality, the mass transport approach has been proven to be an effective and robust tool in geometric inequalities. Stability, on the other hand, requires a more problem-specific approach. In this seminar, we will delve into some of its historical developments and then focus on the proof of the stability of the isoperimetric inequality by Figalli-Maggi and Pratelli. If time permits, we will discuss the stability of Sobolev inequality.