On locally convex hypersurfaces with boundary

Neil S. Trudinger*, Xu Jia Wang

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    34 Citations (Scopus)

    Abstract

    In this paper we give some geometric characterizations of locally convex hypersurfaces. In particular, we prove that for a given locally convex hypersurface M with boundary, there exists r > 0 depending only on the diameter of M and the principal curvatures of M on its boundary, such that the r-neighbourhood of any given point on M is convex. As an application we prove an existence theorem for a Plateau problem for locally convex hypersurfaces of constant Gauss curvature.

    Original languageEnglish
    Pages (from-to)11-32
    Number of pages22
    JournalJournal fur die Reine und Angewandte Mathematik
    Issue number551
    DOIs
    Publication statusPublished - 2002

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