Hilbert manifold structure for asymptotically hyperbolic relativistic initial data

Erwann Delay; Jérémie Fougeirol

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arXiv · 1607.05616

Hilbert manifold structure for asymptotically hyperbolic relativistic initial data

Erwann Delay·Jérémie Fougeirol

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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.

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Erwann Delay, Jérémie Fougeirol. 2016-07-19. Hilbert manifold structure for asymptotically hyperbolic relativistic initial data. https://arxiv.org/abs/1607.05616

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