A sharp quantitative version of Hales' isoperimetric honeycomb theorem

2014/10/22 by Caroccia, Marco, Maggi, Francesco · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1410.6128

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.

Cited by

• Multi-Bubble Isoperimetric Problems

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