Discrete maximal surfaces with singularities in Minkowski space

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• 作者：Masashi Yasumoto ^{myasu@math.kobe-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：53A10 ; 52C99
• 刊名：Differential Geometry and its Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：43
• 期：Complete
• 页码：130-154
• 全文大小：1969 K

文摘

We describe discrete maximal surfaces with singularities in 3-dimensional Minkowski space and give a Weierstrass type representation for them. In the smooth case, maximal surfaces (spacelike surfaces with mean curvature identically 0) in Minkowski 3-space generally have certain singularities. We give a criterion that naturally describes the “singular set” for discrete maximal surfaces, including a classification of the various types of singularities that are possible in the discrete case.