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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.

4 votes
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Do the interiors of curves of constant width admit "linear" measures?

Concise question: In two dimensions, do all shapes of constant width admit a measure over their interior such that for any two parallel lines intersecting the shape, the area between them under the me …
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