English

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}
}
R2 v1 2026-06-28T10:36:31.652Z