Journal of Differential Geometry
- J. Differential Geom.
- Volume 57, Number 2 (2001), 239-271.
Strictly Convex Submanifolds and Hypersurfaces of Positive Curvature
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
