Abstract view
|
Asymptotics of Perimeter-Minimizing Partitions
|
|
Published:2010-05-11
Printed: Sep 2010
Quinn Maurmann,
Department of Mathematics, UCLA, Los Angeles, CA, USA
Max Engelstein,
Department of Mathematics, Yale University, New Haven, CT, USA
Anthony Marcuccio,
Department of Mathematics and Statistics, Williams College, Williamstown, MA, USA
Taryn Pritchard,
Department of Mathematics and Statistics, Williams College, Williamstown, MA, USA
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.
| MSC Classifications: |
53C42 show english descriptions
Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
53C42 - Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
|
