Existence of static vacuum extensions with prescribed Bartnik boundary data
Abstract
We prove the existence and local uniqueness of asymptotically flat, static vacuum metrics with arbitrarily prescribed Bartnik boundary data that are close to the induced boundary data on any star-shaped hypersurface or a general family of perturbed hypersurfaces in the Euclidean space. It confirms the existence part of the Bartnik static extension conjecture for large classes of boundary data, and the static vacuum metric obtained is geometrically unique in a neighborhood of the Euclidean metric.
Keywords
Cite
@article{arxiv.2103.15887,
title = {Existence of static vacuum extensions with prescribed Bartnik boundary data},
author = {Zhongshan An and Lan-Hsuan Huang},
journal= {arXiv preprint arXiv:2103.15887},
year = {2022}
}
Comments
In Version 2, Lemma 4.8 is strengthened. In Version 3, Corollary 8 strengthened to include star-shaped hypersurfaces. We are very grateful to Pengzi Miao for pointing it out. Version 4 matched the version to appear in Cambridge Journal of Mathematics