Asymptotics of Perimeter-Minimizing Partitions
- Autores: Quinn Maurmann, Max Engelstein, Anthony Marcuccio, Taryn Pritchard
- Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 53, Nº 3, 2010, págs. 516-525
- Idioma: inglés
- DOI: 10.4153/cmb-2010-056-x
- Enlaces
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Resumen
We prove that the least perimeter P(n) of a partition of a smooth, compact Riemannian surface into n regions of equal area A is asymptotic to n/2 times the perimeter of a planar regular hexagon of area A. Along the way, we derive tighter estimates for flat tori, Klein bottles, truncated cylinders, and Möbius bands.
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