On the stability of the polygonal isoperimetric inequality
Classical Analysis and ODEs
2014-02-19 v1 Differential Geometry
Abstract
We obtain a sharp lower bound on the isoperimetric deficit of a general polygon in terms of the variance of its side lengths, the variance of its radii, and its deviation from being convex. Our technique involves a functional minimization problem on a suitably constructed compact manifold and is based on the spectral theory for circulant matrices.
Keywords
Cite
@article{arxiv.1402.4460,
title = {On the stability of the polygonal isoperimetric inequality},
author = {Emanuel Indrei and Levon Nurbekyan},
journal= {arXiv preprint arXiv:1402.4460},
year = {2014}
}