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Immersed surfaces of prescribed Gauss curvature into Minkowski space
Author(s):
Yuxin
Ge
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2093-2101.
MSC (2000):
Primary 53C42, 53B25
Posted:
December 7, 2000
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Abstract:
Given a positive real valued function 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 is . Our approach lies on the construction of Gauss map of surfaces.
References:
- 1.
- S. I. Al'ber, Spaces of mappings into a manifold with negative curvature, Dokl. Akad. Nauk. SSSR. Tom 178 (1968), No. 1. MR 37:5817
- 2.
- J. Eells and L. Lemaire, A report on the harmonic maps, Bull. London. Math. Soc 10 (1978), 1-68.
- 3.
- Y. Ge, An elliptic variational approach to immersed surfaces of prescribed Gauss curvature, Calc. Var. 7 (1998) 173-190.
- 4.
- M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. Math. Studies. 105, Princeton. Univ. Press, Princeton (1983). MR 86b:49003
- 5.
- D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Grundlehren. 224, Spinger, Berlin-Heidelberg-New York-Tokyo (1983). MR 86c:35035
- 6.
- P. Hartman, On homotopic harmonic maps, Canad. J. Math. 19 (1967) 673-687. MR 35:4856
- 7.
- P. Hartman and A. Wintner, On the local behavior of solutions of nonparabolic partial differential equations, Amer. J. Math. 75 (1953) 449-476. MR 15:318b
- 8.
- F. Hélein, Applications harmoniques, lois de conservation et repère mobile, Diderot éditeur, Paris-New York-Amsterdam (1996).
- 9.
- J. Jost, Two-dimensional geometric variational problems, Wiley (1991). MR 92h:58045
- 10.
- J. Jost and M. Meier, Boundary regularity for minima of certain quadratic functionals, Math. Ann. 262 (1983) 549-561. MR 84i:35051
- 11.
- H. Lewy, On differential geometry in the large, I (Minkowski's problem), Trans. Amer. Math. Soc. 43 (1938) 258-270. CMP 95:18
- 12.
- C. B. Morrey, Multiple integrals in the calculus of variations, Springer, Grundlehren. 130, New York (1966). MR 34:2380
- 13.
- L. Nirenberg, The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math. 6 (1966), 337-394. MR 15:347b
- 14.
- Stoïlow, Leçons sur les principes topologiques de la théorie des fonctions analytiques, Paris (1938), Gauthier-Villars, p. 130.
- 15.
- M. Struwe, Variational Methods, Springer, Berlin-Heidelberg-New York-Tokyo (1990).
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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:
10.1090/S0002-9939-00-05770-1
PII:
S 0002-9939(00)05770-1
Keywords:
Gauss curvature,
surfaces,
Minkowski space,
harmonic maps
Received by editor(s):
April 29, 1999 and, in revised form, October 20, 1999
Posted:
December 7, 2000
Communicated by:
Bennett Chow
Copyright of article:
Copyright
2000,
American Mathematical Society
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