Volume comparison of conformally compact manifolds with scalar curvature $R\ge -n\left(n-1\right)$

Abstract

In this paper, we use the normalized Ricci-DeTurk flow to prove a stability result for strictly stable conformally compact Einstein manifolds. As an application, we show a local volume comparison of conformally compact manifolds with scalar curvature $R\ge -n\left(n-1\right)$ and also the rigidity result when certain renormalized volume is zero.

27 pages, no figure

References in corpus (1)

• A volume comparison theorem for asymptotically hyperbolic manifolds

Cited by in corpus (1)

• Large isoperimetric regions in asymptotically hyperbolic manifolds