Starshaped compact hypersurfaces with prescirbed Weingarten curvature in warped product manifolds

Daguang Chen; Haizhong Li; Zhizhang Wang

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arXiv · 1705.00313

Starshaped compact hypersurfaces with prescirbed Weingarten curvature in warped product manifolds

Daguang Chen·Haizhong Li·Zhizhang Wang

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Abstract

Given a compact Riemannian manifold $M$, we consider a warped product $\bar M = I \times_h M$ where $I$ is an open interval in $\Bbb R$. For a positive function $\psi$ defined on $\bar M$, we generalized the arguments in \cite{GRW2015} and \cite{RW16}, to obtain the curvature estimates for Hessian equations $\sigma_k(\kappa)=\psi(V,\nu(V))$. We also obtain some existence results for the starshaped compact hypersurface $\Sigma$ satisfying the above equation with various assumptions.

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Daguang Chen, Haizhong Li, Zhizhang Wang. 2017-04-30. Starshaped compact hypersurfaces with prescirbed Weingarten curvature in warped product manifolds. https://arxiv.org/abs/1705.00313

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