Variational problems of Monge-Ampère type

Xu-Jia Wang, Bin Zhou

    Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


    We consider the existence and regularity of maximizers (or minimizers) to two Monge-Ampere type functionals, one is the affine volume functional and the other arises in the study of Calabis extremal metrics on toric Kahler manifolds. The Euler equations of both functionals are fourth order partial differential equations, which are elliptic when the solution is a convex function. Both equations can be written as a system of a Monge-Ampere equation and a linearized Monge-Ampere equation. We discuss recent development on the regularity of maximizers to these two functionals
    Original languageEnglish
    Title of host publicationAMS/IP Studies in Advanced Mathematics, Fifth International Congress of Chinese Mathematicians Part 1
    EditorsLizhen Ji
    Place of PublicationUnited States of America
    PublisherInternational Press
    ISBN (Print)9780821875551
    Publication statusPublished - 2012


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