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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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
Email: Oliver.Schnuerer@mis.mpg.de, schnuere@math.harvard.edu

DOI: https://doi.org/10.1090/S0002-9947-02-03135-5
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