TY - CHAP

T1 - The Anisotropic Total Variation and Surface Area Measures

AU - Rotem, Liran

N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85175070472&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-26300-2_11

DO - 10.1007/978-3-031-26300-2_11

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AN - SCOPUS:85175070472

T3 - Lecture Notes in Mathematics

SP - 297

EP - 312

BT - Lecture Notes in Mathematics

ER -