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
相关论文
共 50 条
  • [31] ON THE REGULARITY OF BOUNDARIES OF SETS MINIMIZING PERIMETER WITH A VOLUME CONSTRAINT
    GONZALEZ, E
    MASSARI, U
    TAMANINI, I
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1983, 32 (01) : 25 - 37
  • [32] Asymptotics for partitions over the Fibonacci numbers and related sequences
    Coons, Michael
    Kristensen, Simon
    Laursen, Mathias L.
    arXiv, 2023,
  • [33] A spectral analogue of the Meinardus theorem on asymptotics of the number of partitions
    Tate, Tatsuya
    ASYMPTOTIC ANALYSIS, 2010, 67 (1-2) : 101 - 123
  • [34] Large m asymptotics for minimal partitions of the Dirichlet eigenvalue
    Zhiyuan Geng
    Fanghua Lin
    Science China(Mathematics), 2022, 65 (01) : 1 - 8
  • [35] Asymptotics of Riemann Sums for Uniform Partitions of Intervals of Integration
    Adam, Marcin
    Ludew, Jakub Jan
    Rozanski, Michal
    Smuda, Adrian
    Witula, Roman
    SYMMETRY-BASEL, 2025, 17 (02):
  • [36] On the Andrews-Zagier asymptotics for partitions without sequences
    Bringmann, Kathrin
    Kane, Ben
    Parry, Daniel
    Rhoades, Robert
    ADVANCES IN MATHEMATICS, 2017, 309 : 436 - 451
  • [37] Large m asymptotics for minimal partitions of the Dirichlet eigenvalue
    Zhiyuan Geng
    Fanghua Lin
    Science China Mathematics, 2022, 65 : 1 - 8
  • [38] The Asymptotics of Plane Partitions with Fixed Volumes of Diagonal Parts
    Bogoliubov N.
    Malyshev C.
    Journal of Mathematical Sciences, 2021, 257 (4) : 469 - 475
  • [39] Large m asymptotics for minimal partitions of the Dirichlet eigenvalue
    Geng, Zhiyuan
    Lin, Fanghua
    SCIENCE CHINA-MATHEMATICS, 2022, 65 (01) : 1 - 8
  • [40] SKEW DOUBLED SHIFTED PLANE PARTITIONS: CALCULUS AND ASYMPTOTICS
    Han, Guo-Niu
    Xiong, Huan
    ELECTRONIC RESEARCH ARCHIVE, 2021, 29 (01): : 1841 - 1857
12345