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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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Jordan measurability of the level sets
Let $A$ be a compact subset of $R^n$ and $d_S(\bullet, A)$ be the
signed distance function of $A$. Namely, $d_S(p,A) =
d\left({p,\partial A} \right)$ for p in A, and $d_S(p,A) =
-d\left({p,\partial A …