The isoperimetric problem for the Favard length

Published 9 Jun 2026 in math.MG | (2606.10608v1)

Abstract: The Favard length of a Borel set $E$ on the Euclidean plane is the average length of its orthogonal projections (mean shadow). Here we solve the following problem: Minimize the Favard length in the class of planar Borel sets with unit area (2-dimensional Lebesgue measure). It is shown that a circle with unit area is a solution, as expected.

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