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Recent advances in Geometric Analysis

Nonlocal minimal cones and a gradient estimate for nonlocal minimal graphs

speaker: Xavier Cabré (ICREA and UPC, Barcelona)

abstract: The talk will be concerned with s-minimal surfaces, that is, hypersurfaces of Rⁿ with zero nonlocal mean curvature. These are the equations associated to critical points of the fractional s-perimeter. We prove that half spaces are the only stable s-minimal cones in R³ for s sufficiently close to 1. We will then turn to nonlocal minimal graphs in any dimension, for which we establish a gradient estimate. It leads to their smoothness, a result that was only known for n=1,2 (but without a quantitative bound); in higher dimensions only their continuity had been established.

timetable:
Tue 5 Jun, 9:00 - 10:00, Aula Dini
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