As in the case of minimal surfaces in the Euclidean 3-space, the reflection principle for maximal surfaces in the Lorentz-Minkowski 3-space asserts that if a maximal surface has a spacelike line segment L , the surface is invariant under the $$180^\circ$$ 180 ∘ -rotation with respect to L . However, such a reflection property does not hold for lightlike line segments on the boundaries of maximal surfaces in general. In this paper, we show some kind of reflection principle for lightlike line segments on the boundaries of maximal surfaces when lightlike line segments are connecting shrinking singularities. As an application, we construct various examples of periodic maximal surfaces with lightlike lines from tessellations of $$\mathbb {R}^2$$ R 2 .

中文翻译：

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最大表面上似光线段的反射原理

与欧几里得 3 空间中的极小曲面的情况一样，洛伦兹-闵可夫斯基 3 空间中极大曲面的反射原理断言，如果极大曲面具有类空间线段 L ，则该曲面在 $$180^ 下是不变的\circ$$ 180 ∘ - 相对于 L 的旋转。然而，这种反射特性通常不适用于最大表面边界上的光状线段。在本文中，我们展示了当类光线段连接收缩奇点时在最大曲面边界上的类光线段的某种反射原理。作为一个应用程序，我们用来自 $$\mathbb {R}^2$$ R 2 的细分的光状线构造了周期性极大曲面的各种示例。