Isoperimetric inequalities for quermassintegrals

Neil S. Trudinger

    Research output: Contribution to journalArticlepeer-review

    66 Citations (Scopus)


    The isoperimetric inequalities of Aleksandrov and Fenchel for quermassintegrals (cross sectional measures) of convex domains in Euclidean space are established for non-convex domains, subject to natural curvature conditions. The techniques are new and draw upon the theory of Monge-Ampère type equations related to previous work of the author on equations of prescribed curvature.

    Original languageEnglish
    Pages (from-to)411-425
    Number of pages15
    JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
    Issue number4
    Publication statusPublished - 1 Jul 1994


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