17 citations · 44 across the 18 of their papers we have counts for
32 papers
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…
Densities in free groups and , Visible Points and Test Elements
Ilya Kapovich, Igor Rivin, Paul Schupp +1
In this article we relate two different densities. Let be the free group of finite rank and let be the abelianization map from onto . We pr…
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…
Estimates and identities for the average distortion of a linear transformation
Igor Rivin
For a linear transformation A from Rn to Rn, we give sharp bounds for the average distortion of A, that is, the average value of log of the euclidean norm of Au over all unit vecto…
Surface area and other measures of ellipsoids
Igor Rivin
We begin by studying the surface area of an ellipsoid in n-dimensional Euclidean space as the function of the lengths of the semi-axes. We write down an explicit formula as an inte…
On some mean matrix inequalities of dynamical interest
Igor Rivin
Let A be an n by n matrix with determinant 1. We show that for all n > 2 there exist dimensional strictly positive constants C_n such that the average over the orthogonal group of…