First variation of functional Wulff shapes

2023/12/18 by Jacopo Ulivelli, Ulivelli, Jacopo · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #49J53 #52A20 #52A38 #Analytic and geometric function theory #Bone Metabolism and Diseases #FOS: Mathematics #Functional Analysis (math.FA) #Inflammatory mediators and NSAID effects #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2312.11172

openalex publication_date 2023/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce functional Wulff shapes based on the classical construction for compact convex sets. With this new tool, we establish a functional version of Aleksandrov's variational lemma in the family of convex functions with compact domain. The resulting formula is then applied to evaluate the first variation of a class of functionals on convex functions. In particular, we extend a recent result by Huang, Liu, Xi, and Zhao.

Cited by

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

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