On the Gaussian Curvature of Maximal Surfaces and the Calabi–Bernstein Theorem
On the Gaussian Curvature of Maximal Surfaces and the Calabi–Bernstein Theorem
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DOI：
10.1017/s0024609301008220
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发表时间：
2001-07
影响因子：
0.9
通讯作者：
L. Alías;B. Palmer
中科院分区：
文献类型：
--
作者：
L. Alías;B. Palmer
本文给出了Lorentz-Minkowski空间L3中极大曲面上Calabi-Bernstein定理的一种新方法。该方法基于L3中最大曲面上测地线盘总曲率的上界，涉及曲面的局部几何形状及其双曲像。作为应用，给出了Calabi-Bernstein定理的一个新的证明。
In this paper, a new approach to the Calabi–Bernstein theorem on maximal surfaces in the Lorentz–Minkowski space L3 is introduced. The approach is based on an upper bound for the total curvature of geodesic discs in a maximal surface in L3, involving the local geometry of the surface and its hyperbolic image. As an application of this, a new proof of the Calabi–Bernstein theorem is provided.