English

Generalizing Andreev's Theorem via circle patterns

Geometric Topology 2023-09-18 v2

Abstract

In this paper we derive an extended Circle Pattern Theorem that allows obtuse overlap angles. As a consequence, we characterize a subclass of compact convex hyperbolic polyhedra with possibly obtuse dihedral angles and thus generalize Andreev's Theorem. For proofs of these results, we establish a discrete analog of the "weak solution/regularity theory" scheme.

Keywords

Cite

@article{arxiv.2308.14386,
  title  = {Generalizing Andreev's Theorem via circle patterns},
  author = {Ze Zhou},
  journal= {arXiv preprint arXiv:2308.14386},
  year   = {2023}
}

Comments

27 pages, 4 figures

R2 v1 2026-06-28T12:05:49.065Z