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

Full Text (PDF format)

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