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arXiv · 1707.00605

Proof of the Honeycomb Asymptotics for Optimal Cheeger Clusters

Dorin Bucur·Ilaria Fragala
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Abstract

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.

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Dorin Bucur, Ilaria Fragala. 2017-06-30. Proof of the Honeycomb Asymptotics for Optimal Cheeger Clusters. https://arxiv.org/abs/1707.00605

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