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Uniqueness of the
Cheeger set of a convex body
Vicent Caselles, Antonin Chambolle and Matteo Novaga |
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Vol. 232 (2007), No. 1, 77–90
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Abstract |
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We prove that if C ⊂ ℝN is of class C2 and uniformly convex, the Cheeger set of C is unique. The Cheeger set of C is the set that minimizes, inside C, the ratio of perimeter over volume. |
Keywords
convex bodies, variational problems
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Mathematical Subject Classification 2000
Primary: 35J70
Secondary: 49J40, 52A20
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Milestones
Received: 6 April 2006
Revised: 21 July 2006
Accepted: 3 August 2006
Published: 1 September 2007
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Authors |
| Vicent Caselles | |
| Departament de Tecnologia Universitat Pompeu Fabra Passeig Circumvallació, 8 08003 Barcelona Spain |
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| Antonin Chambolle | |
| CMAP, École Polytechnique CNRS 91128 Palaiseau France |
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| Matteo Novaga | |
| Dipartimento di Matematica Università di Pisa Largo Bruno Pontecorvo 5 56127 Pisa Italy |
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