English

Least-perimeter partitions of the disk into three regions of given areas

Differential Geometry 2007-05-23 v1

Abstract

We prove that the unique least-perimeter way of partitioning the unit 2-dimensional disk into three regions of prescribed areas is by means of the standard graph consisting in three balanced constant geodesic curvature curves meeting themselves at 120 degrees, and reaching orthogonally the boundary of the disk.

Keywords

Cite

@article{arxiv.math/0307207,
  title  = {Least-perimeter partitions of the disk into three regions of given areas},
  author = {Antonio Cañete and Manuel Ritoré},
  journal= {arXiv preprint arXiv:math/0307207},
  year   = {2007}
}

Comments

19 pages, 8 figures