Paper · May 1, 2021

Prescribed Webster scalar curvature flow on CR manifold

Pak Tung Ho, Quoc Anh Ngo, Hong Zhang

math.DGWider flowsarXiv:2105.00170
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Abstract

Using the prescribed Webster scalar curvature flow, we prove some existence results on the 3-dimensional compact CR manifold with nonnegative CR Yamabe constant.

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Submitted
May 1, 2021
Subjects
math.DG, math.CV
Other curvature flows3-manifoldsScalar curvature

Its neighbourhood

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 Prescribed scalar curvature plus mean curvature flows in compact manifolds with boundary of negative conformal invariant (Xuezhang Chen, Pak Tung Ho and Liming Sun, 2016)5Chen 2016 Prescribed Q-curvature flow on closed manifolds of even dimension (Quôc Anh Ngô and Hong Zhang, 2017)1Ngô 2017 Scalar curvature flow on S^n to a prescribed sign-changing function (Hong Zhang, 2017)2Zhang 2017 A fractional conformal curvature flow on the unit sphere (Xuezhang Chen and Pak Tung Ho, 2019)4Chen 2019 CR Yamabe constant, CR Yamabe flow and its soliton (Pak Tung Ho and Kunbo Wang, 2020)7Ho 2020 Convergence rate of the prescribed curvature flow (Pak Tung Ho and Jinwoo Shin, 2021)3Ho 2021 Legendrian curve flow in Sasakian sub-Riemannian 3-manifolds (Jingshi Cui and Peibiao Zhao, 2025)6Cui 2025 A non-convergence phenomenon for the CR Yamabe flow (Claudio Afeltra, Andrea Pinamonti and Pak Tung Ho, 2026)8Afeltra 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Prescribed -curvature flow on closed manifolds of even dimension

    Quôc Anh Ngô and Hong ZhangWider flows

    Topics Other curvature flows · Same authors Quoc Anh Ngo, Hong Zhang

  2. Scalar curvature flow on S^n to a prescribed sign-changing function

    Hong ZhangWider flows

    Topics Scalar curvature, Other curvature flows · Same author Hong Zhang

  3. Convergence rate of the prescribed curvature flow

    Pak Tung Ho and Jinwoo ShinWider flows

    Topics Scalar curvature, Other curvature flows · Same author Pak Tung Ho · Shared terms “Yamabe”

  4. A fractional conformal curvature flow on the unit sphere

    Xuezhang Chen and Pak Tung HoWider flows

    Topics Scalar curvature, Other curvature flows · Same author Pak Tung Ho

  5. Prescribed scalar curvature plus mean curvature flows in compact manifolds with boundary of negative conformal invariant

    Xuezhang Chen, Pak Tung Ho and Liming SunWider flows

    Topics Scalar curvature · Same author Pak Tung Ho

  6. Legendrian curve flow in Sasakian sub-Riemannian 3-manifolds

    Jingshi Cui and Peibiao ZhaoWider flows

    Topics 3-manifolds, Scalar curvature, Other curvature flows · Shared terms “Webster scalar”

  7. CR Yamabe constant, CR Yamabe flow and its soliton

    Pak Tung Ho and Kunbo WangWider flows

    Same author Pak Tung Ho · Shared terms “Yamabe constant”

  8. A non-convergence phenomenon for the CR Yamabe flow

    Claudio Afeltra, Andrea Pinamonti and Pak Tung HoWider flows

    Topics 3-manifolds · Same author Pak Tung Ho · Shared terms “Yamabe”

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) 3-manifolds Dimension three is where Ricci flow has done its most complete work. It proves geometrization, describes the flow's long-time behaviour, and now… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Scalar curvature The trace of the Ricci tensor. Under Ricci flow its minimum never decreases and positive scalar curvature (PSC) is preserved. Start with: On the proof of the positive mass conjecture in general relativity (Schoen et al., 1979)

In the guidebook

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    A Zoo of Three-ManifoldsBook 10A · Three-Manifolds and Geometrization

    The 3-sphere, lens spaces, the Poincaré sphere, the Hopf fibration and the shape of space.

  2. 10A.2
    Finite Rotation Groups and Spherical Space FormsBook 10A · Three-Manifolds and Geometrization

    Klein's classification by counting poles, the binary groups, and every quotient of the round 3-sphere.

  3. 10A.4
    Homotopy Groups, Degree and the Hurewicz TheoremBook 10A · Three-Manifolds and Geometrization

    Spheres mapped into manifolds: the algebraic topology that finite extinction runs on.