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Polyhomogénéité des métriques asymptotiquement hyperboliques complexes le long du flot de Ricci

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Résumé

On montre que la polyhomogénéité à l’infini d’une métrique asymptotiquement hyperbolique complexe est préservée par le flot de Ricci–DeTurck. De plus, si la métrique initiale est «lisse jusqu’au bord», alors il en sera de même pour les solutions du flot de Ricci normalisé et du flot de Ricci–DeTurck. Lorsque la métrique initiale est aussi kählérienne, des résultats plus précis sont obtenus en termes d’un potentiel.

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  1. Département de Mathématiques, Université du Québec à Montréal, Montreal, QC, Canada

    Frédéric Rochon

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  1. Frédéric Rochon
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Correspondence to Frédéric Rochon.

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Communicated by Ben Andrews.

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Rochon, F. Polyhomogénéité des métriques asymptotiquement hyperboliques complexes le long du flot de Ricci. J Geom Anal 25, 2103–2132 (2015). https://doi.org/10.1007/s12220-014-9505-2

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  • DOI: https://doi.org/10.1007/s12220-014-9505-2

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