17 citations · 48 across the 24 of their papers we have counts for
5 papers · 2 filters
A simpler proof of Mirzakhani's simple curve asymptotics
Igor Rivin
Maryam Mirzakhani (in her doctoral dissertation) has proved the author's conjecture that the number of simple curves of length bounded by L on a hyperbolic surface S is assymptotic…
Volumes and degeneration -- on 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…
Triangulations into Groups
Igor Rivin
If a (cusped) surface S admits an ideal triangulation T with no shears, we show an efficient algorithm to give S as a quotient of hypebolic plane by a subgroup of PSL(2, Z). The al…
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…