Rigidity of non-compact static domains in hyperbolic space via positive mass theorems
Abstract
We single out a notion of staticity which applies to any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For (time-symmetric) initial data sets modeled at infinity on any of these latter examples, we formulate and prove a positive mass theorem in the spin category under natural dominant energy conditions (both in the interior and along the boundary) whose rigidity statement retrieves, among other things, a sharper version of a recent result by Souam to the effect that no such hypersurface admits a compactly supported deformation keeping the original lower bound on the mean curvature. A key ingredient in our approach is the consideration of a family of elliptic boundary conditions on spinors interpolating between chirality and MIT bag boundary conditions.
Keywords
Cite
@article{arxiv.2206.09768,
title = {Rigidity of non-compact static domains in hyperbolic space via positive mass theorems},
author = {Sergio Almaraz and Levi Lopes de Lima},
journal= {arXiv preprint arXiv:2206.09768},
year = {2022}
}
Comments
30 pages, no figures; rewritten at some points to improve the presentation; submitted version