Isoperimetric inequalities for convex hulls and related questions
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- by Paolo Tilli PDF
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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.References
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Additional Information
- Paolo Tilli
- Affiliation: Dipartimento di Matematica, Politecnico di Torino, 10129 Torino, Italy
- Email: paolo.tilli@polito.it
- Received by editor(s): November 22, 2006
- Received by editor(s) in revised form: January 8, 2008
- Published electronically: April 5, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 4497-4509
- MSC (2010): Primary 52A10, 52B60, 52A40
- DOI: https://doi.org/10.1090/S0002-9947-10-04734-3
- MathSciNet review: 2645038