Thu, 06 Jun 2024
12:00
L5

Volume above distance below

Raquel Perales
(CIMAT)
Abstract

Given a pair of metric tensors gj ≥ g0 on a Riemannian manifold, M, it is well known that Volj(M)≥Vol0(M). Furthermore, the volumes are equal if and only if the metric tensors are the same, gj=g0. Here we prove that if for a sequence gj, we have gj≥g0, Volj(M)→Vol0(M) and diam(Mj) ≤ D then (M,gj) converges to (M,g0) in the volume preserving intrinsic flat sense. The previous result will then be applied to prove stability of a class of tori.
 

This talk is based on joint works of myself with: Allen and Sormani (https://arxiv.org/abs/2003.01172), and Cabrera Pacheco and Ketterer (https://arxiv.org/abs/1902.03458).

Song of the Week: Mott the Hoople - All the Young Dudes

David Bowie wrote this song for Mott the Hoople who at the time were about to break up after limited commercial success. Drummer Dale Griffin said that when they heard the song they thought: "He wants to give us that? He must be crazy! We broke our necks to say yes!" Some vintage socks on view as well. 

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