Paper · Dec 21, 2018

Clifford algebra, isoparametric foliation and related geometric constructions

Chao Qian, Zizhou Tang

math.DGWider flowsarXiv:1812.10367
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Abstract

Based on representation theory of Clifford algebra, Ferus, Karcher and Münzner constructed a series of isoparametric foliations. In this paper, we will survey recent studies on isoparametric hypersurfaces of OT-FKM type and investigate related geometric constructions with mean curvature flow.

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Submitted
Dec 21, 2018
Subjects
math.DG

Comments: arXiv admin note: substantial text overlap with arXiv:1407.0539

Mean curvature flow

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Connected papers

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 The mean curvature flow by parallel hypersurfaces (Hiuri Fellipe Santos dos Reis and Keti Tenenblat, 2017)8dos Reis 2017 On Mean curvature flow of Singular Riemannian foliations: Non compact cases (Marcos M. Alexandrino, Leonardo F. Cavenaghi and Icaro Gonçalves, 2019)1Alexandrino 2019 Ancient solutions to mean curvature flow for isoparametric submanifolds (Xiaobo Liu and Chuu-Lian Terng, 2019)7Liu 2019 Polar foliations on symmetric spaces and the mean curvature flow (Xiaobo Liu and Marco Radeschi, 2020)6Liu 2020 Graphical translating solitons for the mean curvature flow and isoparametric functions (Tomoki Fujii, 2021)2Fujii 2021 Isoparametric hypersurfaces of Riemannian manifolds as initial data for the mean curvature flow (Felippe Guimarães, João Batista Marques dos Santos and João Paulo dos Santos, 2022)3Guimarães 2022 Graphical translating solitons for the inverse mean curvature flow and isoparametric functions (Tomoki Fujii, 2022)4Fujii 2022 Mean Curvature Flow for Isoparametric Submanifolds in Hyperbolic Spaces (Xiaobo Liu and Wanxu Yang, 2025)5Liu 2025
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. On Mean curvature flow of Singular Riemannian foliations: Non compact cases

    Marcos M. Alexandrino, Leonardo F. Cavenaghi and Icaro GonçalvesWider flows

    Topics Mean curvature flow · Shared terms “isoparametric foliation”

  2. Graphical translating solitons for the mean curvature flow and isoparametric functions

    Tomoki FujiiWider flows

    Topics Mean curvature flow · Shared terms “isoparametric”, “foliation”

  3. Isoparametric hypersurfaces of Riemannian manifolds as initial data for the mean curvature flow

    Felippe Guimarães, João Batista Marques dos Santos and João Paulo dos SantosWider flows

    Topics Mean curvature flow · Shared terms “isoparametric”

  4. Graphical translating solitons for the inverse mean curvature flow and isoparametric functions

    Tomoki FujiiWider flows

    Topics Mean curvature flow · Shared terms “isoparametric”, “foliation”

  5. Mean Curvature Flow for Isoparametric Submanifolds in Hyperbolic Spaces

    Xiaobo Liu and Wanxu YangWider flows

    Topics Mean curvature flow · Shared terms “isoparametric”

  6. Polar foliations on symmetric spaces and the mean curvature flow

    Xiaobo Liu and Marco RadeschiWider flows

    Topics Mean curvature flow · Shared terms “foliation”, “isoparametric”

  7. Ancient solutions to mean curvature flow for isoparametric submanifolds

    Xiaobo Liu and Chuu-Lian TerngWider flows

    Topics Mean curvature flow · Shared terms “isoparametric”

  8. The mean curvature flow by parallel hypersurfaces

    Hiuri Fellipe Santos dos Reis and Keti TenenblatWider flows

    Topics Mean curvature flow · Shared terms “isoparametric”

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.

Mean curvature flow Wider flows A hypersurface moves in the direction of its mean curvature vector, which decreases area as fast as possible in the L² sense. Start with: Flow by mean curvature of convex surfaces into spheres (Huisken, 1984)

In the guidebook

  1. 6A.10
    Curve Shortening and the First Geometric FlowsBook 6A · The Heat Equation and Its Relatives

    Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.