The Anisotropic Total Variation and Surface Area Measures

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


We prove 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.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
Number of pages16
StatePublished - 2023

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

ASJC Scopus subject areas

  • Algebra and Number Theory


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