A rigidity theorem for surfaces in Schwarzschild manifold

Abstract

In this article, we prove a rigidity theorem for isometric embeddings into the Schwarzschild manifold, by using the variational formula of quasi-local mass.

8 pages

References in corpus (7)

• Isometric embeddings into the Minkowski space and new quasi-local mass
• Curvature estimates for immersed hypersurfaces in Riemannian manifolds
• Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature
• The Weyl problem in warped product space
• Quasi-local energy with respect to a static spacetime
• On Weyl's embedding problem in Riemannian manifolds
• On the Rigidity of Riemannian-Penrose Inequality for Asymptotically Flat 3-manifolds with Corners

Cited by in corpus (2)

• Variation and rigidity of quasi-local mass
• Uniqueness of isometric immersions with the same mean curvature