Curvature estimates for immersed hypersurfaces in Riemannian manifolds

Pengfei Guan McGill University Siyuan Lu McGill University

Analysis of PDEs Differential Geometry mathscidoc:1811.03001

We establish mean curvature estimate for immersed hypersurface with nonnegative extrinsic scalar curvature in Riemannian manifold $(N^{n+1}, \bar g)$ 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 $(\mathbb S^2, g)$ in $3$-dimensional warped product space $(N^3, \bar g)$. We also discuss isometric embedding problem in spaces with horizon in general relativity, like the Anti-de Sitter-Schwarzschild manifolds and the Reissner-Nordstr\"om manifolds.
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@inproceedings{pengfeicurvature,
  title={Curvature estimates for immersed hypersurfaces in Riemannian manifolds},
  author={Pengfei Guan, and Siyuan Lu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181123011218645346177},
}
Pengfei Guan, and Siyuan Lu. Curvature estimates for immersed hypersurfaces in Riemannian manifolds. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181123011218645346177.
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