Alexandrov's Soap Bubble Theorem for Polygons
Analysis of PDEs
2024-06-27 v1 Optimization and Control
Abstract
Regular polygons are characterized as area-constrained critical points of the perimeter functional with respect to particular families of perturbations in the class of polygons with a fixed number of sides. We also review recent results in the literature involving other shape functionals as well as further open problems.
Cite
@article{arxiv.2406.18163,
title = {Alexandrov's Soap Bubble Theorem for Polygons},
author = {Marco Bonacini and Riccardo Cristoferi and Ihsan Topaloglu},
journal= {arXiv preprint arXiv:2406.18163},
year = {2024}
}