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.
Alexandrov’s Soap Bubble Theorem for Polygons / Bonacini, M., Cristoferi, R., Topaloglu, I.. - In: THE AMERICAN MATHEMATICAL MONTHLY. - ISSN 0002-9890. - 132:7(2025), pp. 666-675. [10.1080/00029890.2025.2500881]
Alexandrov’s Soap Bubble Theorem for Polygons
Bonacini M.;Cristoferi R.;
2025-01-01
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.File in questo prodotto:
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