Asymptotics of Perimeter-Minimizing Partitions

被引：0
|
作者：
Maurmann, Quinn [1 ]
Engelstein, Max [2 ]
Marcuccio, Anthony [3 ]
Pritchard, Taryn [3 ]
机构：
[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90024 USA
[2] Yale Univ, Dept Math, New Haven, CT 06520 USA
[3] Williams Coll, Dept Math & Stat, Williamstown, MA 01267 USA
来源：
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2010年 / 53卷 / 03期
基金：
美国国家科学基金会;
关键词：
D O I：
10.4153/CMB-2010-056-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 Mobius bands.
引用
收藏
页码：516 / 525
页数：10
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