On the $m$th-order Affine P\'olya-Szeg\"o Principle
Functional Analysis
2025-06-04 v2 Metric Geometry
Abstract
An affine P\'olya-Szeg\"o principle for a family of affine energies, with equality condition characterization, is demonstrated. In particular, this recovers, as special cases, the affine P\'olya-Szeg\"o principles due to Cianchi, Lutwak, Yang and Zhang, and subsequently Haberl, Schuster and Xiao. Various applications of this new P\'olya-Szeg\"o principle are shown.
Keywords
Cite
@article{arxiv.2409.02232,
title = {On the $m$th-order Affine P\'olya-Szeg\"o Principle},
author = {Dylan Langharst and Michael Roysdon and Yiming Zhao},
journal= {arXiv preprint arXiv:2409.02232},
year = {2025}
}
Comments
26 pages