Lattice Point Asymptotics and Volume Growth on Teichmuller space
Jayadev Athreya, Alexander Bufetov, Alex Eskin, Maryam Mirzakhani
Abstract
We apply some of the ideas of the Ph.D. Thesis of G. A. Margulis to Teichmuller space. Let x be a point in Teichmuller space, and let BR(x) be the ball of radius R centered at x (with distances measured in the Teichmuller metric). We obtain asymptotic formulas as R tends to infinity for the volume of BR(x), and also for for the cardinality of the intersection of BR(x) with an orbit of the mapping class group.
Create a lesson
Related papers
A blueprint for the formalization of norm-variation of multiple ergodic averages for commuting transformations
Floris van Doorn, Polona Durcik, Joris Roos et al.
On some aspects of discrete groups acting ergodically on the boundary
Subhadip Dey, Mikołaj Frączyk, Sebastian Hurtado
A Structural Theory of Admissible Transitions in Biological Reaction Networks
Stephan Peter, Bashar Ibrahim
Sequential and distributive dual futile cycle: Hopf bifurcation can occur under parameter-rich kinetics but cannot occur under mass action kinetics
Nicola Vassena
Rigidity on the two-torus and Sarnak's conjecture
Yinshan Chang, Jian Wang, Junchang Zhou
Linear response for random systems with a cusp
Davrbek Oltiboev, Karim Rakhimov, Marks Ruziboev