An Isoperimetric Inequality for Planar Triangulations

作者:Angel Omer*; Benjamini Itai; Horesh Nizan
来源:Discrete & Computational Geometry, 2018, 59(4): 802-809.
DOI:10.1007/s00454-017-9942-3

摘要

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.

  • 出版日期2018-6