Proof of the Honeycomb Asymptotics for Optimal Cheeger Clusters
Metric Geometry
2017-07-04 v1 Optimization and Control
Spectral Theory
Abstract
We prove that, in the limit as , the hexagonal honeycomb solves the optimal partition problem in which the criterion is minimizing the largest among the Cheeger constants of mutually disjoint cells in a planar domain. As a by-product, the same result holds true when the Cheeger constant is replaced by the first Robin eigenvalue of the Laplacian.
Keywords
Cite
@article{arxiv.1707.00605,
title = {Proof of the Honeycomb Asymptotics for Optimal Cheeger Clusters},
author = {Dorin Bucur and Ilaria Fragala},
journal= {arXiv preprint arXiv:1707.00605},
year = {2017}
}