The stability of Llarull's theorem
Organizers
Speaker
Time
Tuesday, November 19, 2024 3:00 PM - 4:00 PM
Venue
A7-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
Llarull's theorem characterizes the round n-sphere among all spin manifolds whose scalar curvature is bounded from below by n(n-1). We show that if scalar curvature nearly meets this lower bound, n(n-1), then the metric is C^0-close to the round metric outside a small set. This result provides the first instance of a scalar curvature stability theorem that applies in all dimensions, without requiring additional geometric or topological conditions. It is a joint work with Sven Hirsch.
Speaker Intro
I am interested in geometric analysis and general relativity. More specifically, I am working on problems related to scalar curvature and geometric problems from physics. I enjoy applying the tools from PDEs, especially elliptic PDEs, to study geometry.