Work

Differentiability of Lipschitz mappings into metric spaces: area and co-area formulas

Year: 2026

Type: preprint

Abstract: We give a self-contained exposition of metric differentiability for Lipschitz mappings from sets in Euclidean spaces into arbitrary metric spaces, together with the corresponding area and co-area formulas. The novelty is a new metric implicit function theorem for mappings into metric spaces, which is then used to give a direct and geometric proof of the co-area formula for Lipschitz mappings into metric spaces.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.09121

Authors: Esmayli, Behnam, Goldstein, Paweł, Hajłasz, Piotr

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, University of Pittsburgh, Science Foundation Ireland, Ministerstwo Edukacji i Nauki, Uniwersytet Warszawski

Award: Geometric Function Theory: Analysis, Geometry and Topology

OpenAlex ID: W7212006798

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