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Asymptotics of Perimeter-Minimizing Partitions
Published online by Cambridge University Press: 20 November 2018
Abstract
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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- Copyright © Canadian Mathematical Society 2010
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