Geometric applications of Linear and Nonlinear Potential Theory

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