Staticity of Asymptotically Hyperbolic Minimal Mass Extensions
Differential Geometry
2023-05-18 v1
Abstract
In this paper, we give a definition for the Bartnik mass of a domain whose extensions are asymptotically hyperbolic manifolds. With this definition, we show that asymptotically hyperbolic admissible extensions of a domain that achieve the Bartnik mass must admit a static potential. Given a non-static admissible extension of a domain, we are able to construct a one-parameter family of metrics that are close to the original metric, have smaller mass, share the same bound on the scalar curvature, and contain the domain isometrically.
Keywords
Cite
@article{arxiv.2305.09844,
title = {Staticity of Asymptotically Hyperbolic Minimal Mass Extensions},
author = {Daniel Martin},
journal= {arXiv preprint arXiv:2305.09844},
year = {2023}
}