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Transactions of the American Mathematical Society

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A generalized Minkowski problem with Dirichlet boundary condition

Author: Oliver C. Schnurer
Journal: Trans. Amer. Math. Soc. 355 (2003), 655-663
MSC (2000): Primary 35J65; Secondary 53C42
Published electronically: September 6, 2002
MathSciNet review: 1932719
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Abstract: We prove the existence of hypersurfaces with prescribed boundary whose Weingarten curvature equals a given function that depends on the normal of the hypersurface.

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Additional Information

Oliver C. Schnurer
Affiliation: Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22–26, D-04103 Leipzig, Germany
Address at time of publication: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA

Keywords: Minkowski problem, Dirichlet problem, prescribed curvature, convex hypersurfaces
Received by editor(s): November 8, 2000
Published electronically: September 6, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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