Stable Configurations of repelling points on compact hyperbolic Manifolds

TL;DR

This paper demonstrates that on compact hyperbolic manifolds, stable repelling point configurations tend to become uniformly distributed as the number of points grows large.

Contribution

It establishes the equidistribution of stable repelling point configurations on compact hyperbolic manifolds, extending understanding of point dynamics in hyperbolic geometry.

Findings

Stable repelling configurations become equidistributed with increasing points

Configurations maintain stability along all geodesics

Results apply specifically to compact hyperbolic manifolds

Abstract

It is shown that on compact hyperbolic manifolds, certain stable configurations of points which mutually repel along all interconnecting geodesics become equidistributed as the number of points increases