Hilbert manifold structure for weakly asymptotically hyperbolic relativistic initial data. (English) Zbl 1466.83010
Summary: We construct a Hilbert manifold structure à la R. Bartnik [Commun. Anal. Geom. 13, No. 5, 845–885 (2005; Zbl 1123.83006)] for the space of weakly asymptotically hyperbolic initial data for the vacuum constraint equations. The proofs requires new weighted Poincaré and Korn-type inequalities for asymptotically hyperbolic manifolds with inner boundary.
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C40 | Gravitational energy and conservation laws; groups of motions |
| 46T05 | Infinite-dimensional manifolds |
| 53Z05 | Applications of differential geometry to physics |
