Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into ℝⁿ

2022/10/12 by Giacomo Del Nin, Del Nin, Giacomo, Raquel Perales +1
Mathematics · #28A75 (primary) 49Q15 #53C24 (secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2210.06406

openalex publication_date 2022/10/12 · openalex created_date 2022/10/14 · openalex updated_date 2026/07/28

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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