17 citations · 44 across the 18 of their papers we have counts for
6 papers · 1 filter
Extra-large metrics
Igor Rivin
An extra large metric is a spherical cone metric with all cone angles greater than 2 pi and every closed geodesic longer than 2pi. We show that every two-dimensional extra large me…
Continuity of volumes -- on a generalization of a conjecture of J. W. Milnor
Igor Rivin
In his paper "On the Schlafli differential equality", J. Milnor conjectured that the volume of n-dimensional hyperbolic and spherical simplices, as a function of the dihedral angle…
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…
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…
Simple curves on surfaces
Igor Rivin
We show that the number of simple closed geodesics of length bounded by L on a hyperbolic surface of genus g with c cusps and b boundary components grows roughly like L^{6g+2b+2c-6…
Combinatorial optimization in geometry
Igor Rivin
We study the moduli space of euclidean structures with cone points on a surface, and describe a decomposition into cells each of which corresponds to a given combinatorial type of…