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Rigidity of equality cases in Steiner's perimeter inequality
journal contribution
posted on 2023-06-08, 18:44 authored by Filippo Cagnetti, Maria Colombo, Guido De Philippis, Francesco MaggiCharacterization 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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Publication status
- Published
File Version
- Accepted version
Journal
Analysis and PDEISSN
2157-5045Publisher
Mathematical Sciences PublishersExternal DOI
Issue
7Volume
7Page range
1535-1593Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2014-10-20First Open Access (FOA) Date
2014-10-20First Compliant Deposit (FCD) Date
2014-10-20Usage metrics
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