Intrinsic geometry of convex ideal polyhedra in hyperbolic 3-space

2000/05/23 by Igor Rivin · 1 citation
Mathematics · Physics and Astronomy · #math.GT #math-ph #math.CO #math.DG #math.MG #math.MP #msc:52B70 #msc:51M10 #msc:51M20 #msc:52A55 #msc:52B10 #msc:57M50

paper · pdf

published as Analysis, algebra, and computers in mathematical research (Luleå, 1992), 275--291, Lecture Notes in Pure and Appl. Math., 156, Dekker, New York, 1994 · 13 pages; appeared in proceedings of the 1992 nordic math congress; very difficult to find

arxiv created 2000/05/23 · arxiv updated 2009/11/30

Abstract

The main result is that every complete finite area hyperbolic metric on a sphere with punctures can be uniquely realized as the induced metric on the surface of a convex ideal polyhedron in hyperbolic 3-space. A number of other observations are included.

Cited by

• Characterization of Infinite Ideal Polyhedra in Hyperbolic 3-Space via Combinatorial Ricci Flow

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