Conformal compactification of asymptotically locally hyperbolic metrics

Abstract

In this paper we study the extent to which conformally compact asymptotically hyperbolic metrics may be characterized intrinsically. Building on the work of the first author, we prove that decay of sectional curvature to -1 and decay of covariant derivatives of curvature outside an appropriate compact set yield Hölder regularity for a conformal compactification of the metric. In the Einstein case, we prove that the estimate on the sectional curvature implies the control of all covariant derivatives of the Weyl tensor, permitting us to strengthen our result.

References in corpus (1)

• De l'équation de prescription de courbure scalaire aux équations de contrainte en relativité générale sur une variété asymptotiquement hyperbolique

Cited by in corpus (6)

• Ricci flow of conformally compact metrics
• The Jang equation and the positive mass theorem in the asymptotically hyperbolic setting
• Regularity and rigidity of asymptotically hyperbolic manifolds
• Prescribed non positive scalar curvature on asymptotically hyperbolic manifolds with application to the Lichnerowicz equation
• Asymptotic strictly pseudoconvex CR structure for asymptotically locally complex hyperbolic manifolds
• CR compactification for asymptotically locally complex hyperbolic almost Hermitian manifolds