Renormalized volume of minimally bounded regions in asymptotically hyperbolic Einstein spaces
Differential Geometry
2023-08-01 v2 Mathematical Physics
math.MP
Abstract
We define a renormalized volume for a region in an asymptotically hyperbolic Einstein manifold that is bounded by a Graham-Witten minimal surface and the conformal infinity. We prove a Gauss-Bonnet theorem for the renormalized volume, and compute its derivative under variations of the minimal hypersurface.
Keywords
Cite
@article{arxiv.2101.11755,
title = {Renormalized volume of minimally bounded regions in asymptotically hyperbolic Einstein spaces},
author = {Matthew J. Gursky and Stephen E. McKeown and Aaron J. Tyrrell},
journal= {arXiv preprint arXiv:2101.11755},
year = {2023}
}
Comments
39 pages, typos have been fixed and the main calculation in section 4 has been streamlined