论文标题
最大表面上光线段段的反射原理
Reflection principle for lightlike line segments on maximal surfaces
论文作者
论文摘要
就像欧几里得3空间中最小的表面一样，Lorentz-Minkowski中最大表面的反思原理3空间3个空间断言，如果最大表面具有空间式线段$ l $，则表面在$ 180^\ circle $ -Rotation cover-lotation convartiant cop $ l $ a $ $ l $ a $ a $ $ l $中。但是，这种反射属性通常不适合在最大表面的边界上的光线段段。 在本文中，当灯泡线段连接到缩小的奇点时，我们在最大表面边界上显示了某种反射原理。作为一个应用程序，我们构建了各种定期最大表面的示例，并带有$ \ mathbb {r}^2 $的镶嵌线。
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 $180^\circ$-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 $\mathbb{R}^2$.
