Lipschitz-volume rigidity of Lipschitz manifolds among integral currents

2023/02/15 by Roger Züst, Züst, Roger
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2302.07587

openalex publication_date 2023/02/15 · openalex created_date 2023/02/18 · openalex updated_date 2026/07/28

Abstract

We give sufficient conditions such that a volume preserving 1-Lipschitz map from a metric integral current onto an infinitesimally Euclidean Lipschitz manifold is an isometry.

Related

• The Lipschitz-volume rigidity problem for metric manifolds
• Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into ℝⁿ
• Geometric and analytic structures on metric spaces homeomorphic to a manifold
• Lipschitz Chain Approximation of Metric Integral Currents
• Rigidity of Lipschitz map using harmonic map heat flow