On the growth of nonuniform lattices in pinched negatively curved manifolds

TL;DR

This paper investigates how the exponential volume growth rate in pinched negatively curved manifolds relates to the critical exponent of their lattices, linking geometric and dynamical properties.

Contribution

It establishes a connection between volume growth and lattice critical exponents in negatively curved manifolds, advancing understanding of their geometric and dynamical interplay.

Findings

Exponential volume growth rate correlates with lattice critical exponent.

The study reveals new relationships between geometry and geodesic flow dynamics.

Results contribute to the broader understanding of lattice structures in curved spaces.

Abstract

We study the relation between the exponential growth rate of volume in a pinched negatively curved manifold and the critical exponent of its lattices. These objects have a long and interesting story and are closely related to the geometry and the dynamical properties of the geodesic flow of the manifold .