Renormalized Area for Minimal Hypersurfaces of 5D Poincar\'e-Einstein Spaces
Differential Geometry
2023-08-01 v2 Mathematical Physics
math.MP
Abstract
In this paper we derive a Gauss-Bonnet formula for the renormalized area of Graham-Witten minimal hypersurfaces of 5-dimensional Poincar\'e-Einstein spaces. The formula we derive expresses the renormalized area in terms of integrals of pointwise scalar Riemannian invariants. We also prove a result which gives a characterization of minimal hypersurfaces with second fundamental form in terms of conformal geometry at infinity.
Keywords
Cite
@article{arxiv.2204.06663,
title = {Renormalized Area for Minimal Hypersurfaces of 5D Poincar\'e-Einstein Spaces},
author = {Aaron J. Tyrrell},
journal= {arXiv preprint arXiv:2204.06663},
year = {2023}
}
Comments
Typos have been fixed and the second main result has been re-phrased in order to emphasize the fact that it gives a characterization of minimal hypersurfaces with $L^2$ second fundamental form