New variational arguments regarding the Blaschke-Lebesgue theorem

2024/12/18 by Beniamin Bogosel, Bogosel, Beniamin
Biochemistry, Genetics and Molecular Biology · #Dermatological and Skeletal Disorders #Connective tissue disorders research

paper · pdf · doi:10.48550/arxiv.2412.13808

Abstract

The sensitivity of the areas of Reuleaux polygons and disk polygons is computed with respect to vertex perturbations. Computations are completed for both constrained and Lagrangian formulations and they imply that the only critical Reuleaux polygons for the area functional are the regular ones. As a consequence, new variational proofs for the Blaschke-Lebesgue and Firey-Sallee theorems are found.

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