Curvature estimates for immersed hypersurfaces in Riemannian manifolds

• 成果类型: Article
• 署名作者: Guan, Pengfei; Lu, Siyuan
• 署名单位: McGill University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0688-y
• 发表日期: 2017
• 页码: 191-215
• 关键词: nonnegative gauss curvature; quasi-local mass; isometric embeddings; weyl problem; THEOREM

摘要

We establish mean curvature estimate for immersed hypersurface with nonnegative extrinsic scalar curvature in Riemannian manifold (Nn+1,(g) over bar )through regularity study of a degenerate fully nonlinear curvature equation in general Riemannian manifold. The estimate has a direct consequence for the Weyl isometric embedding problem of (S-2, g) in 3-dimensional warped product space (N-3,(g) over bar) . We also discuss isometric embedding problem in spaces with horizon in general relativity, like the Anti-de Sitter-Schwarzschild manifolds and the Reissner-Nordstrom manifolds.