Isoperimetric inequalities for convex hulls and related questions

Tilli, Paolo

doi:10.1090/S0002-9947-10-04734-3

Isoperimetric inequalities for convex hulls and related questions
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Trans. Amer. Math. Soc. 362 (2010), 4497-4509 Request permission

Abstract:

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

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