Euclidean Structures on Simplicial Surfaces and Hyperbolic Volume

@article{Rivin1994EuclideanSO,
  title={Euclidean Structures on Simplicial Surfaces and Hyperbolic Volume},
  author={Igor Rivin},
  journal={Annals of Mathematics},
  year={1994},
  volume={139},
  pages={553-580}
}
  • Igor Rivin
  • Published 1 May 1994
  • Mathematics
  • Annals of Mathematics
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270 Citations
Highly Influential Citations
43
Background Citations
96
Methods Citations
52
Results Citations
13

270 Citations

Citation Type

Citation Type

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A note on complete hyperbolic structures on ideal triangulated 3-manifolds
It is a theorem of Casson and Rivin that the complete hyperbolic metric on a cusp end ideal triangulated 3-manifold maximizes volume in the space of all positive angle structures. We show that the…
Rigidity of Polyhedral Surfaces, III
This paper investigates several global rigidity issues for polyhedral surfaces including inversive distance circle packings. Inversive distance circle packings are polyhedral surfaces introduced by…
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ULLER GEODESICS, DELAUNAY TRIANGULATIONS, AND VEECH GROUPS
In this article, we describe a method for computing generators of the Veech group of a at surface (which we dene as a Riemann surface with a non-zero holomorphic quadratic dierential). The method…
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References

SHOWING 1-5 OF 5 REFERENCES
Hyperbolic geometry: The first 150 years
Singular euclidean structures on surfaces
Geometry of Spaces of Constant Curvature
TLDR
This paper develops elementary geometry in a way very similar to that used to create the geometry the authors learned at school, but since its basic notions can be interpreted in different ways, this geometry can be applied to objects other than the conventional physical space.
On triangulations of surfaces
A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere
We describe a characterization of convex polyhedra in H 3 in terms of their dihedral angles, developed by Rivin. We also describe some geometric and combinatorial consequences of that theory. One of…