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arXiv · 2406.18163

Alexandrov's Soap Bubble Theorem for Polygons

Marco Bonacini·Riccardo Cristoferi·Ihsan Topaloglu
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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.

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Marco Bonacini, Riccardo Cristoferi, Ihsan Topaloglu. 2024-06-26. Alexandrov's Soap Bubble Theorem for Polygons. https://arxiv.org/abs/2406.18163

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