94 research outputs found
Hyperbolic polyhedral surfaces with regular faces
We study hyperbolic polyhedral surfaces with faces isometric to regular
hyperbolic polygons satisfying that the total angles at vertices are at least
The combinatorial information of these surfaces is shown to be
identified with that of Euclidean polyhedral surfaces with negative
combinatorial curvature everywhere. We prove that there is a gap between areas
of non-smooth hyperbolic polyhedral surfaces and the area of smooth hyperbolic
surfaces. The numerical result for the gap is obtained for hyperbolic
polyhedral surfaces, homeomorphic to the double torus, whose 1-skeletons are
cubic graphs.Comment: 23 pages, 3 figures. arXiv admin note: text overlap with
arXiv:1804.1103
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