Decorated discrete conformal maps and convex polyhedral cusps

Autor:	Bobenko, Alexander I., Lutz, Carl O. R.
Rok vydání:	2023
Předmět:	Mathematics - Geometric Topology Mathematics - Metric Geometry 52C26 (Primary) 57M50 52B70 52B10 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We discuss a notion of discrete conformal equivalence for decorated piecewise euclidean surfaces (PE-surface), that is, PE-surfaces with a choice of circle about each vertex. It is closely related to inversive distance and hyperideal circle patterns. Under the assumption that the circles are non-intersecting, we proof the corresponding discrete uniformization theorem. The uniformization theorem for discrete conformal maps corresponds to the special case that all circles degenerate to points. Our proof relies on an intimate relationship between decorated PE-surfaces, canonical tessellations of hyperbolic surfaces and convex hyperbolic polyhedra. It is based on a concave variational principle, which also provides a method for the computation of decorated discrete conformal maps. Comment: 33 pages, 11 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.10988 Zobrazit plný text záznamu View this record from Arxiv