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Convex Hypersurfaces with Prescribed Curvature and Boundary in Riemannian Manifolds

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Abstract

In this article a priori estimates at the boundary for the second fundamental form of n-dimensional convex hypersurfaces M with prescribed curvature quotient Sn (κM)/Sl (κM) in Riemannian manifolds are derived. A consequence of these estimates and other known results is an existence theorem for such hypersurfaces, which is a generalization of a recent result of Ivochkina and Tomi to the Riemannian case.

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  1. Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 288, D-69120, Heidelberg, Germany (E-mail

    Thomas Nehring

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  1. Thomas Nehring
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Nehring, T. Convex Hypersurfaces with Prescribed Curvature and Boundary in Riemannian Manifolds. Annals of Global Analysis and Geometry 17, 77–96 (1999). https://doi.org/10.1023/A:1006589030080

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  • DOI: https://doi.org/10.1023/A:1006589030080

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