Ricci flow of conformally compact metrics. (English. French summary) Zbl 1235.53066
Author’s abstract: “We prove that given a smoothly conformally compact asymptotically hyperbolic metric there is a short-time solution to the Ricci flow that remains smoothly conformally compact and asymptotically hyperbolic. We adapt recent results of O. C. Schnürer, F. Schulze and M. Simon [Commun. Anal. Geom. 16, No. 1, 127–158 (2008; Zbl 1147.53055)] to prove a stability result for conformally compact Einstein metrics sufficiently close to the hyperbolic metric.”
Reviewer: Witold Mozgawa (Lublin)
MSC:
| 53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |
| 58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
| 35K40 | Second-order parabolic systems |
| 35K59 | Quasilinear parabolic equations |
Keywords:
Ricci flow; conformally compact metrics; asymptotically hyperbolic metrics; short time solution; Ricci-DeTurc flowCitations:
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