MathSciDoc: An Archive for Mathematician ∫

 
Log In
Sign Up
Help
Go
 

Starshaped compact hypersurfaces with prescribed Weingarden curvature in warped product manifolds

Daguang Chen Tsinghua University Haizhong Li Tsinghua University Zhizhang Wang Fudan University

Analysis of PDEs Differential Geometry mathscidoc:1810.03003

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
[ Download ] [ 2018-10-30 19:03:08 uploaded by Daguang ] [ 1116 downloads ] [ 0 comments ] 
@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.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved