Hilbert manifold structure for asymptotically hyperbolic relativistic initial data
Differential Geometry
2016-12-15 v2 General Relativity and Quantum Cosmology
Abstract
We provide a Hilbert manifold structure {\`a} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{\'e} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.
Keywords
Cite
@article{arxiv.1607.05616,
title = {Hilbert manifold structure for asymptotically hyperbolic relativistic initial data},
author = {Erwann Delay and Jérémie Fougeirol},
journal= {arXiv preprint arXiv:1607.05616},
year = {2016}
}