2020/07/08 by Matthew J. Gursky, Gursky, Matthew J., Siyi Zhang +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2007.04355
openalex publication_date 2020/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.