The anisotropic total variation and surface area measures

2022/06/27 by Liran Rotem, Rotem, Liran · 3 citations
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Markov Chains and Monte Carlo Methods #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2206.13146

openalex publication_date 2022/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a a formula for the first variation of the integral of a log-concave function, which allows us to define the surface area measure of such a function. The formula holds in complete generality with no regularity assumptions, and is intimately related to the notion of anisotropic total variation and to anisotropic coarea formulas. This improves previous partial results by Colesanti and Fragalà, by Cordero-Erausquin and Klartag and by the author.

Cited by

• Mixed-Derivative Total Variation
• The Gaussian Minkowski problem for epigraphs of convex functions
• A Minkowski problem for α-concave functions via optimal transport

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