Asymptotics of Perimeter-Minimizing Partitions

Canadian mathematical bulletin

Anthony Marcuccio³  Taryn Pritchard³  Quinn Maurmann²  Max Engelstein¹ 

[1] Department of Mathematics, Yale University, New Haven, CT, USA;Department of Mathematics, UCLA, Los Angeles, CA, USA;Department of Mathematics and Statistics, Williams College, Williamstown, MA, USA

关键词: One-dimensional SDEs;    symmetric stable processes;    nonnegative drift;    time change;    integral estimates;    weak convergence;   

DOI  :  10.4153/CMB-2010-056-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 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 Möbius bands.

【 授权许可】

Unknown