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arXiv · 1807.10762

Hyperbolic polyhedral surfaces with regular faces

Yohji Akama·Bobo Hua
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Abstract

We study hyperbolic polyhedral surfaces with faces isometric to regular hyperbolic polygons satisfying that the total angles at vertices are at least $2\pi.$ 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.

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Yohji Akama, Bobo Hua. 2018-07-28. Hyperbolic polyhedral surfaces with regular faces. https://doi.org/10.1016/j.disc.2022.113213.

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