Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds

Claus Gerhardt Ruprecht-Karls-Universität, Institut für Angewandte Mathematik

Differential Geometry mathscidoc:1610.10002

Adv. Calc. Var., 1, 123 - 132, 2008
We prove curvature estimates for general curvature functions. As an application we show the existence of closed, strictly convex hypersurfaces with prescribed curvature $F$, where the defining cone of $F$ is $\C_+$. $F$ is only assumed to be monotone, symmetric, homogeneous of degree $1$, concave and of class $C^{m,\al}$, $m\ge4$.
curvature estimates, Weingarten hypersurface, curvature flows
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@inproceedings{claus2008curvature,
  title={Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds},
  author={Claus Gerhardt},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161002034143233191060},
  booktitle={Adv. Calc. Var.},
  volume={1},
  pages={123 - 132},
  year={2008},
}
Claus Gerhardt. Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds. 2008. Vol. 1. In Adv. Calc. Var.. pp.123 - 132. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161002034143233191060.
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