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
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.