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Questions about geometric properties of sets using measure theoretic techniques; rectifiability of sets and measures, currents, Plateau problem, isoperimetric inequality and related topics.

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References on smoothness of minimal surfaces in Riemannian manifolds

It's well known that $C^1$ minimal surfaces (surfaces that are locally area minimzing) in $\mathbb{R}^n$ are automatically smooth, and one can prove this result by solving the Dirichlet problem of the …