# MathSciDoc: An Archive for Mathematician ∫

#### Distinguished Paper Award in 2018

Calc. Var. Partial Differential Equations, 57, (2), 2018.2
Given a compact Riemannian manifold $M$, we consider a warped product manifold $\bar M = I \times_h M$, where $I$ is an open interval in $\Bbb R$. For a positive function $\psi$ defined on $\bar M$, we generalize 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.
Weingarden curvature, $\sigma_k$, $C^2$ estimates, hypersurfaces
@inproceedings{daguang2018starshaped,
title={Starshaped compact hypersurfaces with prescribed Weingarden curvature in warped product manifolds},
author={Daguang Chen, Haizhong Li, and Zhizhang Wang},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181030190308764772170},
booktitle={ Calc. Var. Partial Differential Equations},
volume={57},
number={2},
year={2018},
}

Daguang Chen, Haizhong Li, and Zhizhang Wang. Starshaped compact hypersurfaces with prescribed Weingarden curvature in warped product manifolds. 2018. Vol. 57. In Calc. Var. Partial Differential Equations. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20181030190308764772170.