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一类相对极值超曲面及其Bernstein性质

A Class of Relative Extremal Hypersurface and Their Bernstein Property
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摘要 在幺模仿射空间定义一个四阶偏微分方程,求出此方程的凸解,证明由此解函数所决定的局部严格凸超曲面的Bernstein性质. In this paper, we first define a forth order PDE on local unimodular affine space of n＋1 and then solve the equation. We investigate locally strong convex hypersurfaces by giving a convex solution of the forth order PDE and prove a Bernstein property of the convex solutions of this equation.
作者 金迎迎 岳洪伟
机构地区 五邑大学数理系 仲恺农业工程学院信息学院
出处 《五邑大学学报（自然科学版）》 CAS 2009年第3期37-41,共5页 Journal of Wuyi University(Natural Science Edition)
关键词 极值超曲面 Bernstein性质 四阶偏微分方程 extremal hypersurface Bernstein property fourth order partial differential equations
分类号 O186.1 [理学—基础数学]
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参考文献8

  • 1LI A M, SIMON U, ZHAO G S. Global affine differential geometry of hypersurfaces [M]. Berlin: Walter de Gruyter, 1993.
  • 2POGORELOV A V. The Minkowski multidimensional problem [M]. Washington D C: V H Winston & Sons, 1978: 39.
  • 3SIMON U. Affine differential geometry [M]//Handbook of differential geometry. Horth-Holland, Amsterndam: Elsevier Science, 2000: 905-961.
  • 4CHERN S S. Affine minimal hypersurfaces [M]//Minimal submanifolds and geodesics. Tokyo: KaigaiPublications, 1978, 17-30.
  • 5LI A M, JIA F. Euclidean complete affine surfaces with constant affine mean curvature[J]. Annals of Global Analysis and Geometry, 2003, 23: 83-304.
  • 6LI A M, JIA F. A Bernstein property of affine maximal hypersurfaces[J]. Annals of Global Analysis and Geometry, 2003, 23: 359-372.
  • 7CALABI Eugenio. Improper affine hyperspheres of convex type and a generalization of a theorem by K Jogens[J]. Michigan Math, 1958, 5: 105-126.
  • 8金迎迎,岳洪伟.统计流形上α-先验的存在性[J].五邑大学学报（自然科学版）,2008,22(3):52-56. 被引量：1

二级参考文献7

  • 1JEFFERYS H. Theory of probability [M]. Berkeley: University of California Press, 1961.
  • 2TAKEUCHI J, AMARI S. α-prior and its properties [J]. IEEE Trans Inform Theory, 2005, 51(3): 1 011-1 023.
  • 3MATSUZOE Hiroshi, TAKEUCHI Jun-ichi, AMARI Shun-ichi. Equiaffine structures on statistical manifolds and Bayesian statistics [J]. Differential Geometry and its Applications, 2006, 24: 567-578.
  • 4NOMIZU K, SASAKI T. Affine differential geometry-geometry of affine immersions [M]. Cambridge: Cambridge University Press. 1994.
  • 5SIMON U. Hypersurfaces in equiaffine differential geometry[J]. Geom Dedicate, 1984, 17: 157-168.
  • 6LAURITZEN S L. Statistical manifolds [M]//AMARI S. Differential geometry in statistical inferences. Haywar California: IMS Lecture Notes Monograph Series, 1987: 96-163.
  • 7LI A M, SIMON U, Zhao G S. Global affine differential geometry of hypersurfaces [M]. Berlin: Walter de Gruyter, 1993.
五邑大学学报（自然科学版）
2009年 第3期

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