### Regularity of minimizing hypersurfaces

Let us consider the following classical problem from geometry (the case \(n=3\) is basically Plateau’s problem): Let \(\Gamma\) be a smooth, closed, oriented, \((n−1\))-dimensional submanifold of \(\mathbb{R}^{n+1}\). If we consider all the smooth, compact, oriented hypersurfaces \(M \subset \mathbb{R}^{n+1}\) with \(\partial M = \Gamma\), does there exist one with least area among them? In the … Continue reading "Regularity of minimizing hypersurfaces"

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