Rigidity for Bach-flat metrics on manifolds with boundary and applications
Differential Geometry
2020-07-21 v2 Analysis of PDEs
Abstract
In the article we consider Bach-flat metrics on four-manifolds with boundary, with conformally invariant boundary conditions. We show that such metrics arise naturally as critical points of the Weyl energy under a constraint. We then prove a rigidity result: if a Yamabe metric associated to a critical metric when restricted to the boundary is isometric to the round three-sphere, then the critical metric must be isometric to the standard upper hemisphere.
Keywords
Cite
@article{arxiv.2007.04355,
title = {Rigidity for Bach-flat metrics on manifolds with boundary and applications},
author = {Matthew J. Gursky and Siyi Zhang},
journal= {arXiv preprint arXiv:2007.04355},
year = {2020}
}
Comments
22 pages, corrected one remark