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Rigidity of equality
cases in Steiner's perimeter inequality
Filippo Cagnetti, Maria Colombo, Guido De Philippis and Francesco Maggi |
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Vol. 7 (2014), No. 7, 1535–1593
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Abstract |
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Characterization results for equality cases and for rigidity of equality cases in Steiner’s perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner symmetral under consideration.) We achieve this through the introduction of a suitable measure-theoretic notion of connectedness and a fine analysis of barycenter functions for sets of finite perimeter having segments as orthogonal sections with respect to a hyperplane. |
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Dedicated to Nicola Fusco, for his mentorship |
Keywords
symmetrization, rigidity, equality cases
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Mathematical Subject Classification 2010
Primary: 49K21
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Milestones
Received: 6 September 2013
Revised: 25 June 2014
Accepted: 11 August 2014
Published: 12 December 2014
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Authors |
| Filippo Cagnetti | |
| Department of Mathematics University of Sussex Pevensey 2 Brighton BN1 9QH United Kingdom |
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| Maria Colombo | |
| Scuola Normale Superiore di
Pisa Piazza dei Cavalieri 7 I-56126 Pisa Italy |
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| Guido De Philippis | |
| Institute for Applied
Mathematics University of Bonn Endenicher Allee 60 D-53115 Bonn Germany |
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| Francesco Maggi | |
| Department of Mathematics The University of Texas at Austin 2515 Speedway Stop C1200 Austin, TX 78712-1202 United States |
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