Pure and Applied Mathematics Quarterly
Volume 17 (2021)
Hilbert manifold structure for weakly asymptotically hyperbolic relativistic initial data
Pages: 443 – 501
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.
Hilbert manifold, asymptotically hyperbolic manifolds, elliptic operators, general relativity, general relativistic constraint equations, weak regularity
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