An interior curvature bound for hypersurfaces of prescribed k-th mean curvature

John Urbas*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    14 Citations (Scopus)

    Abstract

    We derive an interior curvature bound for k-admissible hypersurfaces in ℝn+1 of prescribed k-th mean curvature in terms of the Lp norm of the mean curvature for some p > kn/2. Examples show that in the cases k ≧ 3 such a bound is generally false if p is not sufficiently large.

    Original languageEnglish
    Pages (from-to)41-57
    Number of pages17
    JournalJournal fur die Reine und Angewandte Mathematik
    Volume519
    DOIs
    Publication statusPublished - 2000

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