Proof of the Honeycomb Asymptotics for Optimal Cheeger Clusters

2017/06/30 by Bucur, Dorin, Fragala, Ilaria · 1 citation
#FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1707.00605

Abstract

We prove that, in the limit as k →+ ∞, 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.

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