Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 1

Hilbert manifold structure for weakly asymptotically hyperbolic relativistic initial data

Pages: 443 – 501

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n1.a12

Authors

Erwann Delay (Laboratoire de Mathématiques d’Avignon (EA 2151), Avignon Université, Avignon, France)

Jérémie Fougeirol (Laboratoire de Mathématiques d’Avignon (EA 2151), Avignon Université, Avignon, France)

Abstract

We construct a Hilbert manifold structure à la Bartnik 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.

Keywords

Hilbert manifold, asymptotically hyperbolic manifolds, elliptic operators, general relativity, general relativistic constraint equations, weak regularity

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Erwann Delay was supported by the grant ANR-17-CE40-0034 of the French National Research Agency ANR (project CCEM).

Received 20 March 2020

Accepted 17 December 2020

Published 11 April 2021