English

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}
}