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arXiv · 0704.1021

Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds

Claus Gerhardt
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Abstract

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 $C^{m,\al}$, $m\ge4$.

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Claus Gerhardt. 2008-01-25. Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds. https://doi.org/10.1515/acv.2008.004

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