Paper · Dec 19, 2017

Convergence of the CR Yamabe Flow

Pak Tung Ho, Weimin Sheng, Kunbo Wang

math.DGWider flowsarXiv:1712.06733
View PDF View HTML arXiv page

As on arXiv

Abstract

We consider the CR Yamabe flow on a compact strictly pseudoconvex CR manifold of real dimension . We prove convergence of the CR Yamabe flow when or is spherical.

View PDF View HTML arXiv page
Submitted
Dec 19, 2017
Subjects
math.DG, math.AP, math.CV

Comments: Accepted by Mathematische Annalen

Yamabe flow

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 Convergence of the Yamabe flow on manifolds with minimal boundary (Sergio Almaraz and Liming Sun, 2016)8Almaraz 2016 First eigenvalues of geometric operators under the Yamabe flow (Pak Tung Ho, 2018)6Ho 2018 The Exponential Convergence of the CR Yamabe Flow (Weimin Sheng and Kunbo Wang, 2018)2Sheng 2018 CR Yamabe constant, CR Yamabe flow and its soliton (Pak Tung Ho and Kunbo Wang, 2020)1Ho 2020 Convergence rate of the weighted Yamabe flow (Pak Tung Ho, Jinwoo Shin and Zetian Yan, 2022)4Ho 2022 Convergence rate of the Q-curvature flow (Pak Tung Ho and Sanghoon Lee, 2024)7Ho 2024 Convergence of the fractional Yamabe flow for arbitrary initial energy (Jingeon An-Lacroix, Hardy Chan and Pak Tung Ho, 2025)5An-Lacroix 2025 A non-convergence phenomenon for the CR Yamabe flow (Claudio Afeltra, Andrea Pinamonti and Pak Tung Ho, 2026)3Afeltra 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. CR Yamabe constant, CR Yamabe flow and its soliton

    Pak Tung Ho and Kunbo WangWider flows

    Topics Yamabe flow · Same authors Pak Tung Ho, Kunbo Wang · Shared terms “strictly pseudoconvex”, “compact strictly”

  2. The Exponential Convergence of the CR Yamabe Flow

    Weimin Sheng and Kunbo WangWider flows

    Topics Yamabe flow · Same authors Weimin Sheng, Kunbo Wang

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

    Claudio Afeltra, Andrea Pinamonti and Pak Tung HoWider flows

    Topics Yamabe flow · Same author Pak Tung Ho

  4. Convergence rate of the weighted Yamabe flow

    Pak Tung Ho, Jinwoo Shin and Zetian YanWider flows

    Topics Yamabe flow · Same author Pak Tung Ho

  5. Convergence of the fractional Yamabe flow for arbitrary initial energy

    Jingeon An-Lacroix, Hardy Chan and Pak Tung HoWider flows

    Topics Yamabe flow · Same author Pak Tung Ho

  6. First eigenvalues of geometric operators under the Yamabe flow

    Pak Tung HoWider flows

    Topics Yamabe flow · Same author Pak Tung Ho

  7. Convergence rate of the -curvature flow

    Pak Tung Ho and Sanghoon LeeWider flows

    Topics Yamabe flow · Same author Pak Tung Ho

  8. Convergence of the Yamabe flow on manifolds with minimal boundary

    Sergio Almaraz and Liming SunWider flows

    Topics Yamabe flow

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.

Yamabe flow Wider flows The Yamabe flow deforms a metric inside its conformal class at a rate set by scalar curvature. It is a parabolic approach to the Yamabe problem… Start with: The yamabe flow on locally conformally flat manifolds with positive ricci curvature (Chow, 1992)

In the guidebook

  1. 6C.4
    The Yamabe Problem and Critical ExponentsBook 6C · Nonlinear PDE: Variational and Geometric Methods

    Conformal changes of scalar curvature, the Yamabe functional, Aubin's threshold and Schoen's solution, concentration compactness and bubbles, and why Perelman's log-Sobolev minimisers always exist.