Séance Séminaire

Séminaire Gaston Darboux

Intrinsic conditions for asymptotically hyperbolic metrics.

In this talk I will describe recent work providing intrinsic conditions for complete Riemannian metrics g on noncompact manifolds M to be asymptotically hyperbolic (AH). In particular I assume the existence of an appropriate totally convex set, and sectional curvature decay to -1 along with decay on the first covariant derivative of curvature like that of a smoothly conformally compact AH metric. I use the geometric compactification by asymptotic geodesic rays to compactify M and prove that the compactification has a C^{1,1} structure independent of the totally convex set and that g is Lipschitz conformally compact.