Open AccessMinkowski problem for complete noncompact convex hypersurfaces
Author(s) -
Kai-Seng Chou,
XuJia Wang
Publication year - 1995
Publication title -
topological methods in nonlinear analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.623
H-Index - 23
ISSN - 1230-3429
DOI - 10.12775/tmna.1995.037
Subject(s) - mathematics , hypersurface , mathematical analysis , regular polygon , unit sphere , minkowski space , pure mathematics , curvature , boundary (topology) , gauss , convex function , legendre transformation , geometry , physics , quantum mechanics
We present some sufficient conditions on the existence of a complete noncompactconvex hypersurface whose Gauss curvature is equal to a prescribedfunction on the unit sphere. By the Legendre transform this problem is reducedto the solvability of the Monge-Ampere equation subject to certain boundaryconditions.
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