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Isoperimetric inequalities for convex hulls and related questions
Author(s):
Paolo
Tilli
Journal:
Trans. Amer. Math. Soc.
362
(2010),
4497-4509.
MSC (2010):
Primary 52A10, 52B60, 52A40
Posted:
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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MSC (2010):
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Additional Information:
Paolo
Tilli
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, 10129 Torino, Italy
Email:
paolo.tilli@polito.it
DOI:
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
Posted:
April 5, 2010
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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