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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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Relationship between volume density and area density

Let $\mu(x)dx$ be a measure in $\mathbb{R}^{2n-2}$, where $\mu$ (a $C^\infty$ and positive function) is the density of the volume in the sense that $\DeclareMathOperator{\Vol}{\mathrm{Vol}} \Vol_\mu( …