Periodic maximal surfaces in the Lorentz-Minkowski space L 3
Periodic maximal surfaces in the Lorentz-Minkowski space L 3
复制标题
洛伦兹-闵可夫斯基空间 L 3 中的周期性最大曲面
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
F. J. López
中科院分区：
文献类型：
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作者：
I. Fernández;F. J. López
完备平坦Lorentzian 3-流形N中具有孤立奇点的一个极大曲面S称为整曲面，如果它在L3中提升到一个（周期）整重图S。另外，如果S有有限拓扑，S有2个奇点，且S是一个单重图，则称S是有限型的。N中具有孤立奇点的完全（或真）极大浸入是整的，而N中具有有限个奇点的整嵌入极大曲面是有限型的。本文对带有有限型整极大曲面的完备平坦Lorentzian三维流形进行了分类，并讨论了这类曲面的拓扑、Weierstrass表示和渐近性质。最后，我们构造了L3中基本片具有2个奇异点的周期极大曲面的新例子。
Am aximal surfaceS with isolated singularities in a complete flat Lorentzian 3-manifold N is said to be entire if it lifts to a (periodic) entire multi- graph ˜ S in L 3 . In addition, S is called of finite type if it has finite topology, finitely many singular points and ˜ S is a finitely sheeted multigraph. Complete (or proper) maximal immersions with isolated singularities in N are entire, and entire embed- ded maximal surfaces in N with a finite number of singularities are of finite type. We classify complete flat Lorentzian 3-manifolds carrying entire maximal surfaces of finite type, and deal with the topology, Weierstrass representation and asymptotic behavior of this kind of surfaces. Finally, we construct new examples of periodic en- tire embedded maximal surfaces in L 3 with fundamental piece having finitely many singularities.