Stepanov theorem for mappings between metric spaces

2025/11/19 by Caamaño, Iván
#30L05 #30L99 #51F30 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2511.15907

Abstract

For Lipschitz maps between a metric measure space and a metric space, combining the ideas of Kirchheim's metric differentiability and Cheeger's differentiable structures leads to a Rademacher-type theorem for a notion of metric differentiability with respect to a rectifiable chart, and in this paper we prove the validity of a Stepanov-type generalization of such result under the same assumptions.

Citations

• Connections between metric differentiability and rectifiability
• Abstract and concrete tangent modules on Lipschitz differentiability\n spaces
• Korevaar-Schoen's energy on strongly rectifiable spaces
• Rectifiability of planes and Alberti representations
• On a conjecture of Cheeger
• On the volume measure of non-smooth spaces with Ricci curvature bounded below
• Infinitesimal structure of differentiability spaces, and metric\n differentiation
• Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon Nikodym property

Related

• Connections between metric differentiability and rectifiability
• Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon Nikodym property
• Tangents and rectifiability of Ahlfors regular Lipschitz differentiability spaces
• Lipschitz mappings, metric differentiability, and factorization through metric trees
• The Stepanov theorem for Q-valued functions