Normalized Ricci flows and conformally compact Einstein metrics release_f2hsdrjzrbf5zp7ucsd5we57da

by Jie Qing, Yuguang Shi, Jie Wu

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In this paper, we investigate the behavior of the normalized Ricci flow on asymptotically hyperbolic manifolds. We show that the normalized Ricci flow exists globally and converges to an Einstein metric when starting from a non-degenerate and sufficiently Ricci pinched metric. More importantly we use maximum principles to establish the regularity of conformal compactness along the normalized Ricci flow including that of the limit metric at time infinity. Therefore we are able to recover the existence results in GLLeeBi of conformally compact Einstein metrics with conformal infinities which are perturbations of that of given non-degenerate conformally compact Einstein metrics.
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Type  article
Stage   submitted
Date   2011-06-02
Version   v1
Language   en ?
arXiv  1106.0372v1
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