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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具有边界的紧致奇异极小曲面

摘要：我们根据边界的几何形状研究紧致奇异极小曲面的形状，询问从其边界的知识可以在曲面上获得什么类型的\{\\it apriori\} 信息。我们根据边界推导出面积和高度的估计值。如果边界是圆形，我们研究在什么条件下表面是旋转的。最后，当边界由两条相距足够远的曲线形成时，我们推导出不存在的结果。