Constant curvature foliations on asymptotically hyperbolic spaces
| dc.creator | Mazzeo, Rafe | |
| dc.creator | Pacard, Frank | |
| dc.date | 2007-10-11 | |
| dc.date | 2007-10-12 | |
| dc.date.accessioned | 2026-07-07T08:35:46Z | |
| dc.date.available | 2026-07-07T08:35:46Z | |
| dc.description | Let $(M,g)$ be an asymptotically hyperbolic manifold with a smooth conformal compactification. We establish a general correspondence between semilinear elliptic equations of scalar curvature type on $\del M$ and Weingarten foliations in some neighbourhood of infinity in $M$. We focus mostly on foliations where each leaf has constant mean curvature, though our results apply equally well to foliations where the leaves have constant $σ_k$-curvature. In particular, we prove the existence of a unique foliation near infinity in any quasi-Fuchsian 3-manifold by surfaces with constant Gauss curvature. There is a subtle interplay between the precise terms in the expansion for $g$ and various properties of the foliation. Unlike other recent works in this area, by Rigger \cite{Ri} and Neves-Tian \cite{NT1}, \cite{NT2}, we work in the context of conformally compact spaces, which are more general than perturbations of the AdS-Schwarzschild space, but we do assume a nondegeneracy condition. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0710.2298 | |
| dc.identifier | http://arxiv.org/abs/0710.2298 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139851 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C42; 53C12 | |
| dc.title | Constant curvature foliations on asymptotically hyperbolic spaces | |
| dc.type | text |