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

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 $\H^2$.

arXiv commentI have uploaded the revised vision entitled "Compactness and index of relative equilibria for the curved n-body problem'', which is arXiv:2003.06850