Orlicz–Minkowski flows

Paul Bryan, Mohammad N. Ivaki, Julian Scheuer*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We study the long-time existence and behavior for a class of anisotropic non-homogeneous Gauss curvature flows whose stationary solutions, if they exist, solve the regular Orlicz–Minkowski problems. As an application, we obtain old and new existence results for the regular even Orlicz–Minkowski problems; the corresponding Lp version is the even Lp-Minkowski problem for p> - n- 1. Moreover, employing a parabolic approximation method, we give new proofs of some of the existence results for the general Orlicz–Minkowski problems; the Lp versions are the even Lp-Minkowski problem for p> 0 and the Lp-Minkowski problem for p> 1. In the final section, we use a curvature flow with no global term to solve a class of Lp-Christoffel–Minkowski type problems.

    Original languageEnglish
    Article number41
    Pages (from-to)1-25
    Number of pages25
    JournalCalculus of Variations and Partial Differential Equations
    Volume60
    Issue number1
    DOIs
    Publication statusPublished - Feb 2021

    Bibliographical note

    Copyright the Author(s) 2021. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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