Volume Above Distance Below, Almost Rigidity of Tori, and Intrinsic Flat Convergence
Date:
Wednesday, 12 July, 2023 - 09:00 - 12:00
Venue:
https://cuhk.zoom.us/j/95988240027 (Passcode is six numbers: five-four-nine-seven-zero-eight)
Seminar Type:
CUHK-CUNY-2023 Compactness and Scalar Curvature Workshop
Speaker Name:
Dr. Raquel PERALES
Affiliation:
National Autonomous University of Mexico
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) \leq D then (M,gj) converges to (M,g0) in the volume
preserving intrinsic flat sense. This theorem will then be applied to prove stability of a class
of tori. This talk is be based
on joint work of myself with: Allen and Sormani (https://arxiv.org/abs/2003.01172), and
Cabrera Pacheco and Ketterer (https://arxiv.org/abs/1902.03458).
Poster:
