Given any (not necessarily connected) combinatorial finite graph and any compact smooth 6‐manifold with the third Betti number , we construct a calibrated 3‐dimensional homologically area minimizing surface on equipped in a smooth metric , so that the singular set of the surface is precisely an embedding of this finite graph. Moreover, the calibration form near the singular set is a smoothly twisted special Lagrangian form. The constructions are based on some unpublished ideas of Professor Camillo De Lellis and Professor Robert Bryant.

中文翻译：

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每个有限图都作为紧凑 3D 校准区域最小化表面的奇异集出现

给定任何（不一定连接的）组合有限图和任何具有第三个 Betti 数的紧凑光滑 6 流形，我们构造一个校准的三维同调面积最小化表面，配备光滑度量 ，使得该表面的奇异集为正是这个有限图的嵌入。而且，奇异集附近的标定形式是平滑扭曲的特殊拉格朗日形式。这些结构基于 Camillo De Lellis 教授和 Robert Bryant 教授的一些未发表的想法。