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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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: 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: http://dx.doi.org/10.1090/S0002-9947-10-04734-3
PII: S 0002-9947(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.