Journal of Differential Geometry

Strictly Convex Submanifolds and Hypersurfaces of Positive Curvature

Mohammad Ghomi

Abstract

We construct smooth closed hypersurfaces of positive curvature with prescribed submanifolds and tangent planes. Further, we develop some applications to boundary value problems via Monge-Ampére equations, smoothing of convex polytopes, and an extension of Hadamard's ovaloid theorem to hypersurfaces with boundary.

Article information

Source
J. Differential Geom., Volume 57, Number 2 (2001), 239-271.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090348111

Digital Object Identifier
doi:10.4310/jdg/1090348111

Mathematical Reviews number (MathSciNet)
MR1879227

Zentralblatt MATH identifier
1068.53009

Citation

Ghomi, Mohammad. Strictly Convex Submanifolds and Hypersurfaces of Positive Curvature. J. Differential Geom. 57 (2001), no. 2, 239--271. doi:10.4310/jdg/1090348111. https://projecteuclid.org/euclid.jdg/1090348111


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