A Lower Bound for the Number of Central Configurations on H^2

TL;DR

This paper establishes a lower bound on the number of central configurations in hyperbolic space by analyzing their indices and applying Morse theory, contributing to the understanding of configuration counts in curved spaces.

Contribution

It introduces a novel lower bound for the count of central configurations on hyperbolic space using Morse inequalities and index analysis.

Findings

Central configurations are bounded away from singularities in H^2

A lower bound for the number of configurations is derived

The approach uses Morse theory and index analysis

Abstract

We study the indices of the geodesic central configurations on $\H^2$. We then show that central configurations are bounded away from the singularity set. With Morse's inequality, we get a lower bound for the number of central configurations on $\H^2$.