A sharp quantitative version of Hales' isoperimetric honeycomb theorem
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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.6128
- arXiv:
- arXiv:1410.6128
- Bibcode:
- 2014arXiv1410.6128C
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematics - Metric Geometry;
- Mathematics - Optimization and Control
- E-Print:
- 20 pages, 3 figures