Prescribing singularities of maximal surfaces via a singular Björling representation formula

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• 作者：Young Wook Kim ; Seong-Deog Yang
• 关键词：Maximal surfaces ; Singularities ; Bj&#xf6 ; rling formula
• 刊名：Journal of Geometry and Physics
• 出版年：2007
• 期刊代码：29_03930440
• 类别：ph
• 出版时间：October 2007
• 卷：57
• 期：11
• 页码：2167-2177
• 文件大小：386 K

摘要

We derive a proper formulation of the singular Björling problem for spacelike maximal surfaces with singularities in the Lorentz–Minkowski 3-space which roughly asks whether there exists a maximal surface that contains a prescribed curve as singularities, and then provide a representation formula which solves the problem in an affirmative way. As consequences, we construct many kinds of singularities of maximal surfaces and deduce some properties of the maximal surfaces related to the singularities due to the geometry of the Gauss map.