Spacelike Hypersurfaces of Prescribed Gauss-Kronecker Curvature in Exterior Domains 被引量：1

Spacelike Hypersurfaces of Prescribed Gauss-Kronecker Curvature in Exterior Domains

导出

摘要 In this paper, we prove an existence theorem for spacelike convex hypersurfaces of prescribed Gauss curvature in Minkowski space. In this paper, we prove an existence theorem for spacelike convex hypersurfaces of prescribed Gauss curvature in Minkowski space.

作者 Yong HUANGWuhan Huai Yu JIAN Ning SU

机构地区 Institute of Physics and Mathematics Department of Mathematical Sciences nsu@math

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第3期491-502,共12页 数学学报（英文版）

基金 supported by Tianyuan fund for mathematics (10826060) the third author is partially supported by NSFC under the grant 10471072

关键词 Gauss-Kronecker curvature Minkowski space Monge-Ampere type equation Gauss-Kronecker curvature, Minkowski space, Monge-Ampere type equation

分类号 O186 [理学—基础数学]

引文网络
相关文献

参考文献10

1Finster, F., Schnurer, O. C.: Hypersurfaces of prescribed Gauss curvature in exterior domains. Calc. Vat., 15, 67-80 (2002)
2Cheng, S. Y., Yau, S. T.: Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces. Ann. of Math., 104, 407-419 (1976)
3Guan, B.: The dirichlet problem for Monge-Amperes in non-convex domains and spacelike hypersurfaces of constant gauss curvature. Trans. Amer. Math. Soc., 350, 4955-4971 (1998)
4Guan, B., Jian, H. Y., Schoen, R. M.: Entire spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space. J. fur die reine und angewandte Math., 595, 167-188 (2006)
5Urbas, J.: The Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space. Calc. Var., 18, 307-316 (2003)
6Guan, B., Jian, H. Y.: The Monge-Ampere equation with infinite boundary value. Paci. J. of Math., 216, 77-94 (2004)
7Choi, H. I., Treibergs, A. E.: Gauss maps of spacelike constant mean currvature hypersurface of Minkowski space. J. Diff. Geom., 32, 775-817 (1990)
8Jian, H. Y.: Translating solitions of mean currvature flow of noncompact spacelike hypersurfaces in Minkowski space. J. Diff. Equ., 220, 147-162 (2006)
9Gilbarg, D., Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order, second edition, revised third printing, Springer-Verlag, 1998
10Caffarelli, L., Nirenberg, L., Spruck, J.: The dirichlet problem for nonlinear second-order elliptic equations Ⅰ. Monge-Ampere equation, Comm. Pure Applied Math., 37, 369-402 (1984)

引证文献1

1Yong HUANG.Curvature Estimates of Hypersurfaces in the Minkowski Space[J].Chinese Annals of Mathematics,Series B,2013,34(5):753-764.

1Jeong Ja Bae.GLOBAL EXISTENCE FOR THE NONHOMOGENEOUS QUASILINEAR WAVE EQUATION WITH A LOCALIZED WEAKLY NONLINEAR DISSIPATION IN EXTERIOR DOMAINS[J].Acta Mathematica Scientia,2009,29(5):1203-1215.
2沈一兵,盛卫民.DEFORMING CONVEX HYPERSURFACES BY THE LINEAR COMBINATION OF THE MEAN CURVATURE AND THE N-TH ROOT OF THE GAUSS-KRONECKER CURVATURE[J].Acta Mathematica Scientia,1997,17(2):129-142.
3曾宪忠,刘振海.EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC EQUATIONS IN EXTERIOR DOMAINS[J].Acta Mathematica Scientia,2010,30(3):713-725. 被引量：1
4Zhao Yang YIN.Positive Solutions of a Class of Quasilinear Elliptic Equations in Two-dimensional Exterior Domains[J].Acta Mathematica Sinica,English Series,2006,22(3):819-826.
5Jiajing Miao.On Spacelike Hypersurfaces in Anti de Sitter Four Space[J].数学计算（中英文版）,2014,3(2):30-37.
6Bao Fu WANG.The Affine Complete Hypersurfaces of Constant Gauss-Kronecker Curvature[J].Acta Mathematica Sinica,English Series,2009,25(8):1353-1362.
7Donatella Donatelli,Pierangelo Marcati.LOW MACH NUMBER LIMIT ON EXTERIOR DOMAINS[J].Acta Mathematica Scientia,2012,32(1):164-176.
8Boping TIAN Yongqiang FU.Existence of viscosity solutions for ~Iessian equations in exterior domains[J].Frontiers of Mathematics in China,2014,9(1):201-211. 被引量：1
9张士诚,吴报强.局部对称Lorentz空间中的具有常数量曲率的完备类空超曲面(英文)[J].Chinese Quarterly Journal of Mathematics,2007,22(2):266-275.
10Li Haizhong (Department of Applied Mathematics,Tsinghua University,Beijing 100084,China)(Email:hli@math.tsinghua.edu.cn)Chen Weihuan (Department of Mathematics,Peking University,Beijing 100871,China)(Email:whchen@sxx0.math.pku,edu.cn).Integral Formulas for Compact Spacelike Hypersurfaces in de Sitter Space and their Applications to Goddard's Conjecture[J].Acta Mathematica Sinica,English Series,1998,14(2):285-288. 被引量：10

Acta Mathematica Sinica,English Series

2009年第3期

浏览历史

内容加载中请稍等...

Spacelike Hypersurfaces of Prescribed Gauss-Kronecker Curvature in Exterior Domains 被引量：1

参考文献10

引证文献1

相关作者

相关机构

相关主题

浏览历史