Rigidity of equality cases in steiner's perimeter inequality

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

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    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 languageEnglish (US)
    Pages (from-to)1535-1593
    Number of pages59
    JournalAnalysis and PDE
    Volume7
    Issue number7
    DOIs
    StatePublished - Jan 1 2014

    Fingerprint

    Perimeter
    Rigidity
    Equality
    Connectedness
    Barycentre
    Hyperplane
    Vertical

    Keywords

    • Equality cases
    • Rigidity
    • Symmetrization

    ASJC Scopus subject areas

    • Analysis
    • Numerical Analysis
    • Applied Mathematics

    Cite this

    Cagnetti, F., Colombo, M., De Philippis, G., & Maggi, F. (2014). Rigidity of equality cases in steiner's perimeter inequality. Analysis and PDE, 7(7), 1535-1593. https://doi.org/10.2140/apde.2014.7.1535

    Rigidity of equality cases in steiner's perimeter inequality. / Cagnetti, Filippo; Colombo, Maria; De Philippis, Guido; Maggi, Francesco.

    In: Analysis and PDE, Vol. 7, No. 7, 01.01.2014, p. 1535-1593.

    Research output: Contribution to journalArticle

    Cagnetti, F, Colombo, M, De Philippis, G & Maggi, F 2014, 'Rigidity of equality cases in steiner's perimeter inequality', Analysis and PDE, vol. 7, no. 7, pp. 1535-1593. https://doi.org/10.2140/apde.2014.7.1535
    Cagnetti F, Colombo M, De Philippis G, Maggi F. Rigidity of equality cases in steiner's perimeter inequality. Analysis and PDE. 2014 Jan 1;7(7):1535-1593. https://doi.org/10.2140/apde.2014.7.1535
    Cagnetti, Filippo ; Colombo, Maria ; De Philippis, Guido ; Maggi, Francesco. / Rigidity of equality cases in steiner's perimeter inequality. In: Analysis and PDE. 2014 ; Vol. 7, No. 7. pp. 1535-1593.
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