Polyhomog\'en\'eit\'e des m\'etriques asymptotiquement hyperboliques complexes le long du flot de Ricci

Abstract

We show that the polyhomogeneity at infinity of an asymptotically complex hyperbolic metric is preserved along the Ricci-DeTurck flow. Moreover, if the initial metric is `smooth up to the boundary', this will be preserved by the Ricci-DeTurck flow and the normalized Ricci flow. When the initial metric is K\"ahler, sharper results are obtained in terms of a potential.