An isoperimetric inequality for planar triangulations
Metric Geometry
2016-04-21 v1 Combinatorics
Abstract
We prove a discrete analogue to a classical isoperimetric theorem of Weil for surfaces with non-positive curvature. It is shown that hexagons in the triangular lattice have maximal volume among all sets of a given boundary in any triangulation with minimal degree 6.
Cite
@article{arxiv.1604.05863,
title = {An isoperimetric inequality for planar triangulations},
author = {Omer Angel and Itai Benjamini and Nizan Horesh},
journal= {arXiv preprint arXiv:1604.05863},
year = {2016}
}
Comments
8 pages, 2 figures