Abstract:

We study the shape of a compact singular minimal surface in terms of the geometry of its boundary, asking what type of \{\\it a priori\} information can be obtained on the surface from the knowledge of its boundary. We derive estimates of the area and the height in terms of the boundary. In case that the boundary is a circle, we study under what conditions the surface is rotational. Finally, we deduce non-existence results when the boundary is formed by two curves that are sufficiently far apart.

中文翻译：

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带边界的紧致奇异最小曲面

摘要：

我们根据其边界的几何形状研究紧致奇异最小曲面的形状，询问从其边界的知识可以在表面上获得哪种类型的先验信息。我们根据边界得出面积和高度的估计值。在边界为圆的情况下，我们研究表面在什么条件下旋转。最后，当边界由两条相距足够远的曲线形成边界时，我们推论出不存在的结果。