Scalar curvature deformation and mass rigidity for ALH manifolds with boundary
Differential Geometry
2022-06-08 v2 General Relativity and Quantum Cosmology
Abstract
We study scalar curvature deformation for asymptotically locally hyperbolic (ALH) manifolds with nonempty compact boundary. We show that the scalar curvature map is locally surjective among either (1) the space of metrics that coincide exponentially toward the boundary, or (2) the space of metrics with arbitrarily prescribed nearby Bartnik boundary data. Using those results, we characterize the ALH manifolds that minimize the Wang-Chru\'sciel-Herzlich mass integrals in great generality and establish the rigidity of the positive mass theorems.
Keywords
Cite
@article{arxiv.2108.12887,
title = {Scalar curvature deformation and mass rigidity for ALH manifolds with boundary},
author = {Lan-Hsuan Huang and Hyun Chul Jang},
journal= {arXiv preprint arXiv:2108.12887},
year = {2022}
}
Comments
40 pages; v2: Theorem 1 and Theorem 3 restated. Other main theorems unchanged. The weight spaces slightly modified. Typos corrected. To appear in Trans. Amer. Math. Soc