Calculus of Variations and Geometric Measure Theory

D. Bucur - I. FragalĂ 

Proof of the honeycomb asymptotics for optimal Cheeger clusters

created by bucur on 29 Jun 2017
modified on 30 Jun 2017


Submitted Paper

Inserted: 29 jun 2017
Last Updated: 30 jun 2017

Year: 2017


We prove that, in the limit as $k \to + \infty$, the hexagonal honeycomb solves the optimal partition problem in which the criterion is minimizing the largest among the Cheeger constants of $k$ 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.