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arXiv:0704.1021 [math.DG]AbstractReferencesReviewsResources

Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds

Claus Gerhardt

Published 2007-04-09, updated 2008-01-25Version 2

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

Comments: 9 pages, v2:final version, to be published
Journal: Adv. Calc. Var. 1, 123--132 (2008)
Categories: math.DG
Subjects: 35J60, 53C21, 53C44, 53C50, 58J05
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