Rigidity of equality cases in steiner's perimeter inequality

Filippo Cagnetti; Maria Colombo; Guido De Philippis; Francesco Maggi

doi:10.2140/apde.2014.7.1535

Rigidity of equality cases in steiner's perimeter inequality

Filippo Cagnetti, Maria Colombo, Guido De Philippis, Francesco Maggi

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	1535-1593
Number of pages	59
Journal	Analysis and PDE
Volume	7
Issue number	7
DOIs	https://doi.org/10.2140/apde.2014.7.1535
State	Published - 2014

Keywords

Equality cases
Rigidity
Symmetrization

ASJC Scopus subject areas

Analysis
Numerical Analysis
Applied Mathematics

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10.2140/apde.2014.7.1535

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abstract = "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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AU - Colombo, Maria

AU - De Philippis, Guido

AU - Maggi, Francesco

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Y1 - 2014

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AB - 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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KW - Rigidity

KW - Symmetrization

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Rigidity of equality cases in steiner's perimeter inequality

Abstract

Keywords

ASJC Scopus subject areas

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