Ricci flow of conformally compact metrics
Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 6, pp. 813-835.

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.

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.

DOI : https://doi.org/10.1016/j.anihpc.2011.03.007
Classification : 53C44,  58J35,  35K40,  35K59
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},
zbl = {1235.53066},
mrnumber = {2859929},
language = {en},
url = {http://archive.numdam.org/item/AIHPC_2011__28_6_813_0/}
}
Bahuaud, Eric. Ricci flow of conformally compact metrics. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 6, pp. 813-835. doi : 10.1016/j.anihpc.2011.03.007. http://archive.numdam.org/item/AIHPC_2011__28_6_813_0/

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