Hessian measures on the Heisenberg group

Neil S. Trudinger*, Wei Zhang

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    In this paper, we study the properties of k-convex functions on the Heisenberg group Hn, for 1 ≤ k≤ 2n and prove the weak continuity of k-Hessian measures with respect to local uniform convergence in the Heisenberg setting. Our approach through monotonicity formulae makes use of previous research in the corresponding Euclidean case of Trudinger and Wang. The case k=2. n provides an analogue of the Monge-Ampère measure of Aleksandrov for Hn. We also answer a conjecture of Garofalo and Tournier on monotonicity for the cases n>2.

    Original languageEnglish
    Pages (from-to)2335-2355
    Number of pages21
    JournalJournal of Functional Analysis
    Volume264
    Issue number10
    DOIs
    Publication statusPublished - 15 May 2013

    Fingerprint

    Dive into the research topics of 'Hessian measures on the Heisenberg group'. Together they form a unique fingerprint.

    Cite this