A quantitative metric differentiation theorem

2011/11/10 by Azzam, Jonas, Schul, Raanan · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1111.2561

Abstract

The purpose of this note is to point out a simple consequence of some earlier work of the authors, "Hard Sard: Quantitative implicit function and extension theorems for Lipschitz maps". For f, a Lipschitz function from a Euclidean space into a metric space, we give quantitative estimates for how often the pullback of the metric under f is approximately a seminorm. This is a quantitative version of Kirchheim's metric differentiation result from 1994. Our result is in the form of a Carleson-type estimate.

Cited by

• The Heinonen-Semmes problems after thirty years

Related

• Quantitative decompositions of Lipschitz mappings into metric spaces
• Another introduction to the geometry of metric spaces
• Weak derivatives and metric differentiability almost everywhere
• Comparison Between Teichmuller and Lipschitz Metrics
• An implicit function theorem for Lipschitz mappings into metric spaces