New variational arguments regarding the Blaschke-Lebesgue theorem
Metric Geometry
2024-12-19 v1 Optimization and Control
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.
Cite
@article{arxiv.2412.13808,
title = {New variational arguments regarding the Blaschke-Lebesgue theorem},
author = {Beniamin Bogosel},
journal= {arXiv preprint arXiv:2412.13808},
year = {2024}
}