Stable Configurations of repelling Points on compact Manifolds

TL;DR

This paper demonstrates that on certain compact manifolds, stable repelling point configurations tend to become evenly distributed as the number of points grows, using advanced geometric and spectral analysis techniques.

Contribution

It introduces a differential-geometric approach to analyze stable repelling configurations on compact manifolds, extending classical electrostatics concepts.

Findings

Stable configurations become equidistributed with increasing points

Uses spectral geometry and trace formulas for analysis

Provides a geometric framework for repelling point distributions

Abstract

This is an expanded version of [arXiv:1107.4836v1 [math.DS]]. Using techniques from [Chapter XI, The Selberg Trace Formula, in Eigenvalues in Riemannian Geometry, by Isaac Chavel], in which a differential-geometrically intrinsic treatment of counterparts of classical electrostatics was introduced, it is shown that on some compact manifolds, certain stable configurations of points which mutually repel along all interconnecting geodesics become equidistributed as the number of points increases.