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In this paper, we use the normalized Ricci-DeTurk flow to prove a stabilityresult for strictly stable conformally compact Einstein manifolds. As anapplication, we show a local volume comparison of conformally compact manifoldswith scalar curvature $R\geq -n\left(n-1\right)$ and also the rigidity resultwhen certain renormalized volume is zero.

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