Calculus of Variations and Geometric Measure Theory

G. Del Nin - R. Perales

Rigidity of mass-preserving $1$-Lipschitz maps from integral current spaces into $\mathbb{R}^n$

created by delnin on 24 Oct 2022
modified on 21 Apr 2023

[BibTeX]

Accepted Paper

Inserted: 24 oct 2022
Last Updated: 21 apr 2023

Journal: J. Math. Anal. Appl.
Volume: 526
Number: 1
Year: 2023
Doi: https://doi.org/10.1016/j.jmaa.2023.127297

ArXiv: 2210.06406 PDF

Abstract:

We prove that given an $n$-dimensional integral current space and a $1$-Lipschitz map from this space onto the $n$-dimensional Euclidean ball that preserves the mass of the current and is injective on the boundary then the map has to be an isometry. Then we show how to apply this result to prove the stability of the positive mass theorem for graphical manifolds as originally stated by Huang--Lee--Sormani.