Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds

Abstract

We prove that for a compact 3-manifold M with boundary admitting an ideal triangulation T with valence at least 10 at all edges, there exists a unique complete hyperbolic metric with totally geodesic boundary, so that T is isotopic to a geometric decomposition of M. Our approach is to use a variant of the combinatorial Ricci flow introduced by Luo [Luo05] for pseudo 3-manifolds. In this case, we prove that the extended Ricci flow converges to the hyperbolic metric exponentially fast.

arXiv comment31 pages. This is a revision of the paper

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Cited by in corpus (2)

• Rigidity of discrete conformal structures on surfaces
• Combinatorial Ricci flows with applications to the hyperbolization of cusped 3-manifolds