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Hilbert manifold structure for asymptotically hyperbolic relativistic initial data

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Abstract

We provide a Hilbert manifold structure à la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincaré and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.
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Dates and versions

hal-01346853 , version 1 (19-07-2016)
hal-01346853 , version 2 (13-12-2016)

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Attribution - NoDerivatives - CC BY 4.0

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Erwann Delay, Jérémie Fougeirol. Hilbert manifold structure for asymptotically hyperbolic relativistic initial data. 2016. ⟨hal-01346853v2⟩
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