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 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.
Isoperimetric inequalities for convex hullsand related questions / Tilli, Paolo. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 362:9(2010), pp. 4497-4509.
Isoperimetric inequalities for convex hullsand related questions
TILLI, PAOLO
2010
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 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.Pubblicazioni consigliate
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https://hdl.handle.net/11583/1670543
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