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Curvature and Geometry of Tessellating Plane Graphs

Baues, O.; Peyerimhoff, N.


O. Baues


We show that the growth of plane tessellations and their edge graphs may be controlled from below by upper bounds for the combinatorial curvature. Under the assumption that every geodesic path may be extended to infinity we provide explicit estimates of the grwoth rate and isoperimetric constant of distance ball in negatively curved tessellations. We show that the assumption about geodesics holds for all tessellations with at least p faces meeting in each vertex and at least q edges bounding each face, where (p,q) equals (3,6), (4,4) or (6,3).


Baues, O., & Peyerimhoff, N. (2001). Curvature and Geometry of Tessellating Plane Graphs. Discrete & Computational Geometry, 25(1), 141-159.

Journal Article Type Article
Online Publication Date Jan 1, 2001
Publication Date 2001-01
Journal Discrete and Computational Geometry
Print ISSN 0179-5376
Publisher Springer
Volume 25
Issue 1
Pages 141-159