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arXiv · 1410.6128

A sharp quantitative version of Hales' isoperimetric honeycomb theorem

Marco Caroccia·Francesco Maggi
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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.

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Marco Caroccia, Francesco Maggi. 2014-10-22. A sharp quantitative version of Hales' isoperimetric honeycomb theorem. https://arxiv.org/abs/1410.6128

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