The Gauss image of entire graphs of higher codimension and Bernstein type theorems
The Gauss image of entire graphs of higher codimension and Bernstein type theorems
复制标题
DOI：
10.1007/s00526-012-0533-0
复制
发表时间：
2010-09
影响因子：
2.1
通讯作者：
Juergen Jost;Y. Xin;Ling Yang;Ling Yang
中科院分区：
文献类型：
--
作者：
Juergen Jost;Y. Xin;Ling Yang;Ling Yang
在欧氏空间中具有平行平均曲率完备子流形的Gauss映射值域的适当条件下，构造了一个强次调和函数，并给出了调和Gauss映射的先验估计.这里所需的条件比以前的工作更一般，因此，它们使我们能够大大提高以前的结果的劳森-Osseman问题的最小子流形的正则性在较高的余维，并得出伯恩斯坦型的结果。
Under suitable conditions on the range of the Gauss map of a complete submanifold of Euclidean space with parallel mean curvature, we construct a strongly subharmonic function and derive a-priori estimates for the harmonic Gauss map. The required conditions here are more general than in previous work and they therefore enable us to improve substantially previous results for the Lawson–Osseman problem concerning the regularity of minimal submanifolds in higher codimension and to derive Bernstein type results.