First variation of functional Wulff shapes
Metric Geometry
2024-05-28 v2 Functional Analysis
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.
Cite
@article{arxiv.2312.11172,
title = {First variation of functional Wulff shapes},
author = {Jacopo Ulivelli},
journal= {arXiv preprint arXiv:2312.11172},
year = {2024}
}
Comments
Adjusted hypothesis on the family of perturbations. Section 3 rewritten and Section 5 removed. Comments are welcome