Lipschitz-volume rigidity of Lipschitz manifolds among integral currents

TL;DR

This paper establishes conditions under which a volume-preserving 1-Lipschitz map from an integral current to a Lipschitz manifold must be an isometry, linking Lipschitz volume rigidity to geometric structure.

Contribution

It provides new sufficient conditions for Lipschitz-volume rigidity of maps between integral currents and Lipschitz manifolds, extending rigidity results in metric geometry.

Findings

Volume-preserving 1-Lipschitz maps are isometries under certain conditions

Characterization of Lipschitz-volume rigidity in metric integral currents

Extension of rigidity results to infinitesimally Euclidean Lipschitz manifolds

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.