Starshaped compact hypersurfaces with prescirbed Weingarten curvature in warped product manifolds

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 $\mathbb{R}$. 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.

References in corpus (2)

• Curvature estimates for immersed hypersurfaces in Riemannian manifolds
• On the curvature estimates for Hessian equations

Cited by in corpus (4)

• The curvature estimates for convex solutions of some fully nonlinear Hessian type equations
• A class of prescribed Weingarten curvature equations in Euclidean space
• Mean Curvature Type Flows of Graphs in Product Manifolds
• A class of Hessian quotient equations in the warped product manifold