具有负常数相对仿射平均曲率的欧氏完备超曲面(英文) 被引量：1

The Euclidean complete hypersurfaces with negative constant relative affine mean curvature

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摘要对于一个给定的凸域ΩRn及光滑边值φ∈C∞(■),通过解一类非线性四阶偏微分方程,作者构造了具有负常数相对仿射平均曲率L<0的欧氏完备超曲面. A Euclidean complete hypersurface with constant relative affine mean curvature L 〈 0 is constructed by solving a class 4-order PDE, for a given bounded convex domain Ω beling to R^n and a boundary value φ∈C^∞（^-Ω）.

作者王宝富许瑞伟

机构地区四川大学数学学院

出处《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2008年第5期1001-1006,共6页 Journal of Sichuan University(Natural Science Edition)

基金国家自然科学基金(10771146)

关键词欧氏完备 Monge—Ampère方程 euclidean complete, Monge-ampère equation

分类号 O186.1 [理学—基础数学]

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参考文献10

1Li A M, Simon U, Zhao G S. Global affine differential geometry of hypersurfaces [ M ]. Berlin/New York: Wde Gruyter, 1993.
2Li A M, Simon U, Zhao G S. Hypersurfaces with prescribed affine Gauss-Kronecker curvature[J]. Geometriae Dedicata, 2000, 81: 141.
3Li A M, Jia F. Euclidean complete affine surfaces with constant affine mean curvature [ J ]. Annals of global analysis and geometry, 2003, 23: 283.
4Li A M, Jia F. A Bernstein property of affine maximal hypersurfaces[J]. Annals of Global Analysis and Geomety, 2003, 23: 359.
5Li A M, Simon U, Chen B H. A two-step MongeAmpere procedure for solving a fourth order PDE for affine hypersurfaces with constant constant curvature [J]. Jrein Angew Math, 1997, 487: 179.
6Xu R W. Bernstein properties for some relative parabolic affine hyperspheres[J]. Results in Math, 2008, 52: 409.
7Wang B F, Li A M. The Euclidean complete affine hypersurfaces with negative constant affine mean curvature [J]. Results in Math, 2008, 52: 383.
8Wang B F. The affine complete hypersurfaces of con- stant Gauss-Kronecker curvature [ J ]. Acta Math Sin Eng Sci, Preprint.
9王宝富.具给定仿射曲率的仿射完备的超曲面(英文)[J].四川大学学报（自然科学版）,2007,44(4):729-732. 被引量：1
10杨宝莹,王宝富.仿射Khler流形的一类变分问题(英文)[J].四川大学学报（自然科学版）,2008,45(1):1-9. 被引量：3

二级参考文献12

1Li A M,Udo Simon,Chen B H.A two step Monge-Ampère procedure for solving a fourth order PDE for affine hypersurfaces with constant curvature[J].J Reine Angew Math,1997,487:179.
2Li A M,Udo Simon,Zhao G S.Hypersurfaces with prescribed affine Gauss-Kronecker curvature[J].Geometriae Dedicata,2000,81:141.
3Wang B F,Li A M.The complete affine hypersurface with negative constant affine mean curvature[J].Math Ann,Preprint.
4Wang B F.The affine completeness of constant GaussKronecher curvature[J].Acta Math Sin:Eng Sci,Preprint.
5Cheng S Y, Yau S T. On the real Monge-Ampere equation and affine flat structure[ C]//Chern S S, Wu W T. The 1980 Beijing Symposium Differential Geometry and Differential Equations. Beijing: Science Press, 1982.
6Trudinger N S, Wang X J, The Affine Plateau problem [J].J Amer Math Soc, 2005,18.253.
7Karp L. Subharmonic functions, harmonic mappings and isometric immersions[ C]//Yau S T. Seminar on Differential Geometry. USA: Princeton Univrsity Press, 1982.
8Li A M, Simon U, Zhao G S. Global differential geometry of hypersurfaces[ M]. Berlin/New York:Walter de Gruyter, 1993.
9Calabi E. Hypersurfaces with maximal affinely invariant area[J]. Amer J Math, 1982,104:91.
10Caffarelli L, Nirenbern L, Spruck J. The Dirichlet problem for nonlinear second-order elliptic equations (1), Monge-Amp6re equation [ J ]. Comm Pure Appl Math, 1984,37 : 369.

共引文献2

1陈刚,许瑞伟.中心仿射超曲面的一类变分问题(英文)[J].四川大学学报（自然科学版）,2009,46(3):548-552.
2蒋研,许瑞伟.关于一类四阶偏微分方程解的一个Bernstein性质(英文)[J].四川大学学报（自然科学版）,2010,47(3):420-424.

同被引文献15

1Donaldson S K. Interior estimates for solutions of Abreuts equation, airXiv: math. DG/0407486.
2Jia F, Li A M. Interior estimates for solutions of a fourth order nonlinear partial differential equation [J]. Diff Geom Appl, 2007, 25. 433.
3Li A M, Jia F. Euclidean complete affine surfaces with constant affine mean curvature[J]. Ann Global Anal Geom, 2003, 23: 283.
4Li A M, Jia F. The Bernstein property of some fourth order partial differential equations[J]. Result Math, in press.
5Li A M, Jia F. A Bernstein property of affine maximal hypersurfaces [J]. Ann Global Anal Geom, 2003, 23: 359.
6Li A M, Simon U, Chen B. A two-step Monge- Ampere procedure for solving a fourth order PDE for affine hypersurfaces with constant eurvature[J]. J Reine Angew Math, 1997, 487: 179.
7Li A M, Simon U, Zhao G. Global affine differential geometry of hypersurfaces[M]. Berlin/New York: Walter de Gruyter, 1993.
8Abreu M. K/ihler geometry of toric varieties and extremal metrics[J]. IntJ Math, 1998, 9: 641.
9Xu R W. Bernstein properties for some relative parabolic affine hyperspheres[J]. Result Math, 2008, 52 : 409.
10Trudinger N, Wang X. The Bernstein problem for affine maximal hypersurfaces [J]. Invent Math, 2000, 140: 399.

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8韩英波.具有双不变度量的李群中超曲面的广义Gauss映照[J].高校应用数学学报（A辑）,2008,23(3):373-378.
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