A sharp quantitative version of Hales' isoperimetric honeycomb theorem
Analysis of PDEs
2014-10-23 v1 Metric Geometry
Optimization and Control
Abstract
We prove a sharp quantitative version of Hales' isoperimetric honeycomb theorem by exploiting a quantitative isoperimetric inequality for polygons and an improved convergence theorem for planar bubble clusters. Further applications include the description of isoperimetric tilings of the torus with respect to almost unit-area constraints or with respect to almost flat Riemannian metrics.
Cite
@article{arxiv.1410.6128,
title = {A sharp quantitative version of Hales' isoperimetric honeycomb theorem},
author = {Marco Caroccia and Francesco Maggi},
journal= {arXiv preprint arXiv:1410.6128},
year = {2014}
}
Comments
20 pages, 3 figures