Intrinsic geometry of convex ideal polyhedra in hyperbolic 3-space

Igor Rivin

Intrinsic geometry of convex ideal polyhedra in hyperbolic 3-space

Geometric Topology 2007-05-23 v1 Mathematical Physics Combinatorics Differential Geometry Metric Geometry math.MP

Authors: Igor Rivin

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.

Keywords

convex ideal polyhedra hyperbolic 3-space intrinsic geometry induced metric finite area hyperbolic metric

Cite

@article{arxiv.math/0005234,
  title  = {Intrinsic geometry of convex ideal polyhedra in hyperbolic 3-space},
  author = {Igor Rivin},
  journal= {arXiv preprint arXiv:math/0005234},
  year   = {2007}
}

Comments

13 pages; appeared in proceedings of the 1992 nordic math congress; very difficult to find

Intrinsic geometry of convex ideal polyhedra in hyperbolic 3-space

Abstract

Keywords

Cite

Comments

Related papers