Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds

Details Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds

2007-04-09

arxiv.org/abs/0704.1021v2

Adv. Calc. Var. 1, 123--132 (2008)

Mathematics

Differential Geometry

9 pages, v2:final version, to be published

Scientific paper

10.1515/ACV.2008.004

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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