Effective equidistribution of intersection points in hyperbolic manifolds

TL;DR

This paper proves that intersection points between certain submanifolds in hyperbolic manifolds become uniformly distributed as their volume increases, providing an effective rate of convergence.

Contribution

It introduces a new effective equidistribution result for intersection points in hyperbolic manifolds, extending previous qualitative understandings.

Findings

Effective equidistribution established

Convergence rate quantified

Applicable to finite-volume hyperbolic manifolds

Abstract

In this paper, we establish effective equidistribution of transverse intersection points between properly immersed totally geodesic submanifolds of complementary dimensions in a finite-volume hyperbolic manifold with respect to the hyperbolic volume measure, as the volume of the submanifolds tends to infinity.