Two rigidity results for surfaces in Schwarzschild spacetimes

2023/06/13 by Chen, Po-Ning, Wang, Ye-Kai
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.07477

Abstract

We prove two rigidity results for surfaces lying in the standard null hypersurfaces of Schwarzschild spacetime satisfying certain mean curvature type equations. The first is for the equation α_H = - dlog |H| studied in \citeWWZ. The second is for the mean curvature vector of constant norm. The latter is related to the Liouville and Obata Theorem in conformal geometry.

Related

• A rigidity theorem for surfaces in Schwarzschild manifold
• Stability and rigidity of extremal surfaces in Riemannian geometry and General Relativity
• Rigidity phenomena involving scalar curvature
• Boundary behaviors of spacelike constant mean curvature surfaces in Schwarzschild spacetime
• Uniqueness of isometric immersions with the same mean curvature