On the Gaussian curvature of maximal surfaces and the Calabi-Bernstein theorem

被引：34

作者：

Alías, LJ ^{[1
]}

Palmer, B

机构：

[1] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain

[2] Univ Durham, Dept Math Sci, Durham DH1 3LE, England

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2001年 / 33卷

关键词：

D O I：

10.1017/S0024609301008220

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a new approach to the Calabi-Bernstein theorem on maximal surfaces in the Lorentz-Minkowski space L-3 is introduced. The approach is based on an upper bound for the total curvature of geodesic discs in a maximal surface in L-3, 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.

引用

页码：454 / 458

页数：5

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