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.

A sharp quantitative version of Hales' isoperimetric honeycomb theorem

Caroccia M.;
2016

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.
JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES
Hales' honeycomb theorem
Isoperimetric problems
Partitioning problems
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1174054
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