Pengfei GuanMcGill UniversitySiyuan LuMcGill University
Analysis of PDEsDifferential Geometrymathscidoc: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.
@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.