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math.GT2000
Intrinsic geometry of convex ideal polyhedra in hyperbolic 3-space
Igor Rivin
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 poly…
math.GT2000
A norm on homology of surfaces and counting simple geodesics
Greg McShane, Igor Rivin
We define a norm on homology of punctured tori equipped with a complete hyperbolic metric of finite volume and use it to find asymptotics on the growth of the number of simple geod…
math.CO2000
Extremal metrics on graphs I
Dmitry Jakobson, Igor Rivin
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces…