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

Giacomo Del Nin; Raquel Perales

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arXiv · 2210.06406

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

Giacomo Del Nin·Raquel Perales

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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. We deduce as a consequence a stability result with respect to the intrinsic flat distance, which implies the stability of the positive mass theorem for graphical manifolds as originally formulated by Huang--Lee--Sormani.

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BibTeX RIS

Giacomo Del Nin, Raquel Perales. 2022-10-12. Rigidity of mass-preserving $1$-Lipschitz maps from integral current spaces into $\mathbb{R}^n$. https://arxiv.org/abs/2210.06406

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