Paper · May 29, 2020

Christoffel-Minkowski flows

Paul Bryan, Mohammad N. Ivaki, Julian Scheuer

math.DGWider flowsarXiv:2005.14680
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Abstract

We provide a curvature flow approach to the regular Christoffel-Minkowski problem. The speed of our curvature flow is of an entropy preserving type and contains a global term.

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Submitted
May 29, 2020
Subjects
math.DG, math.AP, math.MG
Journal
Trans. Am. Math. Soc. 376, no. 4, p. 2373-2393, (2023)
DOI
10.1090/tran/8683

Comments: 25 pages

Other curvature flowsGauss curvature flow

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The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper A unified flow approach to smooth, even Lₚ-Minkowski problems (Paul Bryan, Mohammad N. Ivaki and Julian Scheuer, 2016)5Bryan 2016 A class of anisotropic expanding curvature flows (Weimin Sheng and Caihong Yi, 2019)8Sheng 2019 A curvature flow approach to Lp-Christoffel-Minkowski problem for p>1 (Li Chen, Qiang Tu and Ni Xiang, 2019)2Chen 2019 Parabolic approaches to curvature equations (Paul Bryan, Mohammad N. Ivaki and Julian Scheuer, 2020)3Bryan 2020 Orlicz-Minkowski flows (Paul Bryan, Mohammad N. Ivaki and Julian Scheuer, 2020)1Bryan 2020 An expanding curvature flow and the (p,q)-Christoffel-Minkowski problems (Bin Chen, Jingshi Cui and Peibiao Zhao, 2022)4Chen 2022 A flow method for a generalization of Lₚ Christofell-Minkowski problem (Boya Li, Hongjie Ju and Yannan Liu, 2022)6Li 2022 Uniqueness of solutions to a class of isotropic curvature problems (Mohammad N. Ivaki and Emanuel Milman, 2023)7Ivaki 2023
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Orlicz-Minkowski flows

    Paul Bryan, Mohammad N. Ivaki and Julian ScheuerWider flows

    Topics Gauss curvature flow, Other curvature flows · Same authors Paul Bryan, Mohammad N. Ivaki, Julian Scheuer · Shared terms “Minkowski flow”, “Christoffel Minkowski”, “global term”

  2. A curvature flow approach to Lp-Christoffel-Minkowski problem for p>1

    Li Chen, Qiang Tu and Ni XiangWider flows

    Topics Gauss curvature flow, Other curvature flows · Shared terms “Christoffel Minkowski”

  3. Parabolic approaches to curvature equations

    Paul Bryan, Mohammad N. Ivaki and Julian ScheuerWider flows

    Topics Gauss curvature flow, Other curvature flows · Same authors Paul Bryan, Mohammad N. Ivaki, Julian Scheuer · Shared terms “Christoffel Minkowski”, “global term”

  4. An expanding curvature flow and the (p,q)-Christoffel-Minkowski problems

    Bin Chen, Jingshi Cui and Peibiao ZhaoWider flows

    Topics Gauss curvature flow, Other curvature flows · Shared terms “Christoffel Minkowski”

  5. A unified flow approach to smooth, even -Minkowski problems

    Paul Bryan, Mohammad N. Ivaki and Julian ScheuerWider flows

    Topics Gauss curvature flow, Other curvature flows · Same authors Paul Bryan, Mohammad N. Ivaki, Julian Scheuer · Shared terms “Minkowski”

  6. A flow method for a generalization of Christofell-Minkowski problem

    Boya Li, Hongjie Ju and Yannan LiuWider flows

    Topics Gauss curvature flow, Other curvature flows · Shared terms “Christoffel Minkowski”

  7. Uniqueness of solutions to a class of isotropic curvature problems

    Mohammad N. Ivaki and Emanuel MilmanWider flows

    Topics Gauss curvature flow, Other curvature flows · Same author Mohammad N. Ivaki · Shared terms “Christoffel Minkowski”

  8. A class of anisotropic expanding curvature flows

    Weimin Sheng and Caihong YiWider flows

    Topics Gauss curvature flow, Other curvature flows · Shared terms “Christoffel Minkowski”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Other curvature flows Wider flows Flows that move a hypersurface or metric by some other function of curvature: Gauss curvature (worn stones), inverse mean curvature (the Penrose… Start with: Shapes of worn stones (Firey, 1974) Gauss curvature flow Wider flows Convex hypersurfaces shrink with normal speed a power K^α of their Gauss curvature. Firey proposed it as a model of stones worn by waves; for α>… Start with: Shapes of worn stones (Firey, 1974)