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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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Metric measure spaces: in what sense is analysis on these spaces "non-smooth"
I highly recommend the survey article "Nonsmooth Calculus" by Juha Heinonen, available here.
The beginning of the introduction reads:
"The word nonsmooth in the title refers both to functions an …