On stability of the hyperbolic space form under the normalized Ricci flow

Abstract

This paper studies the normalized Ricci flow from a slight perturbation of the hyperbolic metric on ${\mathbb{H}}^n$. It's proved that if the perturbation is small and decays sufficiently fast at the infinity, then the flow will converge exponentially fast to the hyperbolic metric when the dimension $n>5$.

17 pages