Bernstein theorem and regularity for a class of monge-ampère equations

Huaiyu Jian, Xu Jia Wang

    Research output: Contribution to journalArticlepeer-review

    47 Citations (Scopus)

    Abstract

    In this paper we first introduce a transform for convex functions and use it to prove a Bernstein theorem for a Monge-Ampère equation in half space.We then prove the optimal global regularity for a class of Monge-Ampère type equations arising in a number of geometric problems such as Poincaré metrics, hyperbolic affine spheres, and Minkowski type problems.

    Original languageEnglish
    Pages (from-to)431-469
    Number of pages39
    JournalJournal of Differential Geometry
    Volume93
    Issue number3
    DOIs
    Publication statusPublished - 2013

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