Conformal compactification of asymptotically locally hyperbolic metrics II: Weakly ALH metrics

Romain Gicquaud (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

In this paper we pursue the work initiated in \cite{Bahuaud, BahuaudGicquaud}: study the extent to which conformally compact asymptotically hyperbolic metrics can be characterized intrinsically. We show how the decay rate of the sectional curvature to -1 controls the Hölder regularity of the compactified metric. To this end, we construct harmonic coordinates that satisfy some Neumann-type condition at infinity. Combined with a new integration argument, this permits us to recover to a large extent our previous result without any decay assumption on the covariant derivatives of the Riemann tensor. We believe that our result is optimal.

Domaines: Géométrie différentielle [math.DG]; Equations aux dérivées partielles [math.AP]

Romain Gicquaud. Conformal compactification of asymptotically locally hyperbolic metrics II: Weakly ALH metrics. Communications in Partial Differential Equations, 2013, 38 (8), pp.1313-1367. ⟨10.1080/03605302.2013.795966⟩. ⟨hal-00783625⟩