Isoperimetric inequalities for convex hulls and related questions

Author:
Paolo Tilli

Journal:
Trans. Amer. Math. Soc. **362** (2010), 4497-4509

MSC (2010):
Primary 52A10, 52B60, 52A40

Published electronically:
April 5, 2010

MathSciNet review:
2645038

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Paolo Tilli**

Affiliation:
Dipartimento di Matematica, Politecnico di Torino, 10129 Torino, Italy

Email:
paolo.tilli@polito.it

DOI:
https://doi.org/10.1090/S0002-9947-10-04734-3

Received by editor(s):
November 22, 2006

Received by editor(s) in revised form:
January 8, 2008

Published electronically:
April 5, 2010

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.