Geometric applications of Linear and Nonlinear Potential Theory

Cycle 32th Oral Defence of the Phd Thesis

13 February
Versione stampabile

Venue: Povo Zero, via Sommarive 14 (Povo) – Seminar Room “-1”
Time: 11.00 

  • Mattia Fogagnolo - PhD in Mathematics

Abstract

We provide geometric inequalities on Euclidean space and on general manifolds with nonnegative Ricci curvature by employing suitable monotone quantities along the flow of capacitary and p-capacitary potentials, as well as through related boundary value problems. Among the main achievements, we cite:

  1. a Willmore-type inequality on manifolds with nonnegative Ricci curvature leading in turn to the sharp Isoperimetric Inequality on 3-manifolds with nonnegative Ricci curvature;
  2. enhanced Kasue/Croke-Kleiner splitting theorems;
  3. a generalised Minkowski-type inequality in Rn holding with no assumptions on the boundary of the domain considered except for smoothness;
  4. a complete discussion of maximal volume solutions to the least area problem with obstacle on Riemannian manifolds and its relation with the variational p-capacity.

Supervisor: Lorenzo Mazzieri