In this paper 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 Schnürer, Schulze and Simon to prove a stability result for conformally compact Einstein metrics sufficiently close to the hyperbolic metric.
Lʼobjectif de cet article est de démontrer lʼexistence dʼune solution en temps court du flot de Ricci dans la classe de métriques régulières, conformément compactes et asymptotiquement hyperboliques. Nous appliquons ensuite les résultats de Schnürer, Schulze et Simon pour prouver la stabilité des métriques dʼEinstein conformément compactes suffisamment proches de la métrique hyperbolique.
Mots-clés : Ricci flow, Conformally compact metrics, Asymptotically hyperbolic metrics
@article{AIHPC_2011__28_6_813_0, author = {Bahuaud, Eric}, title = {Ricci flow of conformally compact metrics}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {813--835}, publisher = {Elsevier}, volume = {28}, number = {6}, year = {2011}, doi = {10.1016/j.anihpc.2011.03.007}, mrnumber = {2859929}, zbl = {1235.53066}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2011.03.007/} }
TY - JOUR AU - Bahuaud, Eric TI - Ricci flow of conformally compact metrics JO - Annales de l'I.H.P. Analyse non linéaire PY - 2011 SP - 813 EP - 835 VL - 28 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2011.03.007/ DO - 10.1016/j.anihpc.2011.03.007 LA - en ID - AIHPC_2011__28_6_813_0 ER -
Bahuaud, Eric. Ricci flow of conformally compact metrics. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 6, pp. 813-835. doi : 10.1016/j.anihpc.2011.03.007. http://www.numdam.org/articles/10.1016/j.anihpc.2011.03.007/
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