Published Paper

Inserted: 22 oct 2014
Last Updated: 27 oct 2017

Journal: Journal de Mathématiques Pures et Appliquées
Year: 2015

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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• honeycomb_stability6.pdf