The Weyl problem in warped product space

Abstract

In this paper, we discuss the Weyl problem in warped product space. We obtain the openness, non rigidity and some applications. These results together with the a priori estimates obtained by Lu imply some existence results. Meanwhile we reprove the infinitesimal rigidity in the space forms.

References in corpus (2)

• Positivity of Quasilocal Mass
• Quasilocal mass in general relativity

Cited by in corpus (7)

• Curvature estimates for immersed hypersurfaces in Riemannian manifolds
• Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature
• Quasi-local energy with respect to a static spacetime
• A rigidity theorem for surfaces in Schwarzschild manifold
• Variation and rigidity of quasi-local mass
• A quasi-local Penrose inequality for the quasi-local energy with static references
• Uniqueness of isometric immersions with the same mean curvature