Wasserstein Distance and the Rectifiability of Doubling Measures: Part II

2014/11/10 by Jonas Azzam, Guy David, Azzam, Jonas +3
Mathematics · #28Exx #Advanced Harmonic Analysis Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Analysis and Transform Methods #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.MG #msc:28Exx

paper · pdf · doi:10.48550/arxiv.1411.2512

arxiv created 2014/11/10 · openalex publication_date 2014/11/10 · arxiv updated 2014/11/11 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We study the structure of the support of a doubling measure by analyzing its self-similarity properties, which we estimate using a variant of the L¹ Wasserstein distance. We show that measure satisfying certain self-similarity conditions admits a unique (up to multiplication by a constant) flat tangent measure at almost every point. This allows us to decompose the support into rectifiable pieces of various dimensions.

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