Isoperimetric inequalities for convex hulls and related questions
نویسنده
چکیده
We consider the problem of maximizing the Lebesgue measure of the convex hull of a connected compact set of prescribed onedimensional Hausdorff measure. In dimension two, we prove that the only solutions are semicircles. In higher dimension, we prove some isoperimetric inequalities for the convex hull of connected sets, we focus on a classical open problem and we discuss a new possible approach.
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