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An isoperimetric inequality for planar triangulations

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arxiv 1604.05863 v1 pith:4BHL643Y submitted 2016-04-20 math.MG math.CO

Omer Angel , Itai Benjamini , Nizan Horesh This is my paper · ORCID
classification math.MGmath.CO
keywords isoperimetricanalogueboundaryclassicalcurvaturedegreediscretegiven
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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.

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