Asymptotics of perimeter-minimizing partitions

Quinn Maurmann, Max Engelstein, Anthony Marcuccio, Taryn Pritchard

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)516-525
Number of pages10
JournalCanadian Mathematical Bulletin
Volume53
Issue number3
DOIs
StatePublished - Sep 1 2010
Externally publishedYes

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