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Asymptotics of Perimeter-Minimizing Partitions

Published online by Cambridge University Press:  20 November 2018

Quinn Maurmann ,
Max Engelstein ,
Anthony Marcuccio  and
Taryn Pritchard
Quinn Maurmann
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA, U.S.A. e-mail: qmaurmann@math.ucla.edu
Max Engelstein
Affiliation:
Department of Mathematics, Yale University, New Haven, CT, U.S.A.e-mail: max.engelstein@yale.edu
Anthony Marcuccio
Affiliation:
Department of Mathematics and Statistics, Williams College, Williamstown, MA, U.S.A. e-mail: 08anm@williams.edu, 08tbp@williams.edu
Taryn Pritchard
Affiliation:
Department of Mathematics and Statistics, Williams College, Williamstown, MA, U.S.A. e-mail: 08anm@williams.edu, 08tbp@williams.edu
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Abstract

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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.

Keywords

53C42
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 3 , 01 September 2010 , pp. 516 - 525
Copyright
Copyright © Canadian Mathematical Society 2010

References

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