A Minkowski-type inequality in the AdS-Melvin space
Differential Geometry
2021-11-22 v1 General Relativity and Quantum Cosmology
Abstract
The AdS-Melvin spacetime was introduced by Astorino and models the AdS soliton with electromagnetic charge. It is a static spacetime with a time-symmetric Cauchy hypersurface, which we refer to as the AdS-Melvin space. In this paper, we study a sharp Minkowski-type inequality for surfaces embedded in the AdS-Melvin space. We first prove the inequality for special cases in which the surface enjoys axisymmetry or is a small perturbation of a coordinate torus. We then use a weighted normal flow to show that the inequality holds for general surfaces.
Keywords
Cite
@article{arxiv.2111.10287,
title = {A Minkowski-type inequality in the AdS-Melvin space},
author = {Daniel Xia and Pei-Ken Hung},
journal= {arXiv preprint arXiv:2111.10287},
year = {2021}
}