双曲空间的图状极小超曲面  

GRAPH-LIKE MINIMAL HYPERSURFACES IN HYPERBOLIC SPACE

作　　者：张宗劳[1] 

机构地区：[1]温州师范学院数学系,浙江温州325000

出　　处：《安徽师范大学学报（自然科学版）》2005年第2期127-130,共4页Journal of Anhui Normal University(Natural Science)

基　　金：温州师范学院科研基金重点课题资助项目(2003Z12).

摘　　要：给出了双曲空间在上半空间模型下的图状超曲面的概念,提出并研究了双曲空间的图状超曲面的Bernstein问题.借助于Nitsche新近使用的双曲空间的一个新模型,证明了双曲空间中定义在整个双曲超平面上的径向对称极小辐射图一定是双曲超平面,这样就在一定条件下给出了双曲空间的Bernstein问题一个肯定的回答.<Abstrcat> In this paper, with respect to the upper halfspace model, the concept of graph-like hypersurfaces in hyperbolic space is defined, the Bernstein problem of graph-like hypersurfaces in hyperbolic space is formed and investigated. By means of a new model of hyperbolic space used by Nitsche, it is proved that a radially symmetric minimal radial graph in hyperbolic space defined on the whole of a hyperbolic hyperplane is a hyperbolic hyperplane, and this is an affirmative answer to the Bernstein problem in hyperbolic space under some conditions.

关 键 词：双曲空间 极小超曲面 BERNSTEIN 空间模型 径向对称 超平面 新模型 辐射图 

分 类 号：O186.12[理学—数学] O186.11[理学—基础数学]