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Immersed surfaces of prescribed Gauss curvature into Minkowski space


Author: Yuxin Ge
Journal: Proc. Amer. Math. Soc. 129 (2001), 2093-2101
MSC (2000): Primary 53C42, 53B25
Published electronically: December 7, 2000
MathSciNet review: 1825922
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Abstract: Given a positive real valued function $k(x)$ on the disc, we will immerse the disc into three dimensional Minkowski space in such a way that Gauss curvature at the image point of $x$ is $-k(x)$. Our approach lies on the construction of Gauss map of surfaces.


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Additional Information

Yuxin Ge
Affiliation: Département de Mathématiques, Faculté de Sciences et Technologie, Université Paris XII-Val de Marne, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France; C.M.L.A., E.N.S de Cachan, 61, avenue du Président Wilson, 94235 Cachan Cedex, France
Email: ge@cmla.ens-cachan.fr

DOI: https://doi.org/10.1090/S0002-9939-00-05770-1
Keywords: Gauss curvature, surfaces, Minkowski space, harmonic maps
Received by editor(s): April 29, 1999
Received by editor(s) in revised form: October 20, 1999
Published electronically: December 7, 2000
Communicated by: Bennett Chow
Article copyright: © Copyright 2000 American Mathematical Society