Paper · Jul 4, 2020

CR Yamabe constant, CR Yamabe flow and its soliton

Pak Tung Ho, Kunbo Wang

math.DGWider flowsarXiv:2007.02019
View PDF View HTML arXiv page

As on arXiv

Abstract

On a compact strictly pseudoconvex CR manifold , we consider the CR Yamabe constant of its infinite conformal covering. By using the maximum principles, we then prove a uniqueness theorem for the CR Yamabe flow on a complete noncompact CR manifold. Finally we obtain some properties of the CR Yamabe soliton on complete noncompact CR manifolds.

View PDF View HTML arXiv page
Submitted
Jul 4, 2020
Subjects
math.DG

Comments: To appear in NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

Yamabe flowAlmost & η-Ricci solitonsStability & uniquenessBoundaries & non-compact

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 CR Yamabe Flow (Pak Tung Ho, Weimin Sheng and Kunbo Wang, 2017)1Ho 2017 First eigenvalues of geometric operators under the Yamabe flow (Pak Tung Ho, 2018)5Ho 2018 The Exponential Convergence of the CR Yamabe Flow (Weimin Sheng and Kunbo Wang, 2018)8Sheng 2018 Rigidity results for quotient almost Yamabe solitons (Marcelo Bezerra Barboza, Willian Isao Tokura, Elismar Dias Batista et al., 2020)3Barboza 2020 Infinite-time incompleteness of noncompact Yamabe flow (Jin Takahashi and Hikaru Yamamoto, 2021)7Takahashi 2021 The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant (Gilles Carron, Eric Chen and Yi Wang, 2022)2Carron 2022 Convergence rate of the weighted Yamabe flow (Pak Tung Ho, Jinwoo Shin and Zetian Yan, 2022)6Ho 2022 A non-convergence phenomenon for the CR Yamabe flow (Claudio Afeltra, Andrea Pinamonti and Pak Tung Ho, 2026)4Afeltra 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Convergence of the CR Yamabe Flow

    Pak Tung Ho, Weimin Sheng and Kunbo WangWider flows

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

  2. The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant

    Gilles Carron, Eric Chen and Yi WangWider flows

    Topics Yamabe flow, Boundaries & non-compact · Shared terms “Yamabe constant”

  3. Rigidity results for quotient almost Yamabe solitons

    Marcelo Bezerra Barboza, Willian Isao Tokura, Elismar Dias Batista et al.Wider flows

    Topics Yamabe flow, Almost & η-Ricci solitons, Boundaries & non-compact

  4. 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

  5. First eigenvalues of geometric operators under the Yamabe flow

    Pak Tung HoWider flows

    Topics Yamabe flow, Boundaries & non-compact · Same author Pak Tung Ho

  6. Convergence rate of the weighted Yamabe flow

    Pak Tung Ho, Jinwoo Shin and Zetian YanWider flows

    Topics Yamabe flow · Same author Pak Tung Ho

  7. Infinite-time incompleteness of noncompact Yamabe flow

    Jin Takahashi and Hikaru YamamotoWider flows

    Topics Yamabe flow, Boundaries & non-compact · Shared terms “infinite”

  8. The Exponential Convergence of the CR Yamabe Flow

    Weimin Sheng and Kunbo WangWider flows

    Topics Yamabe flow · Same author Kunbo Wang

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) Almost & η-Ricci solitons Variations on the Ricci soliton equation: let the constant λ become a function (almost solitons), add a term along a contact form (η-Ricci… Start with: Ricci almost solitons (Pigola et al., 2010) Stability & uniqueness When does a flow started near a special solution stay near it, and when is a flow determined by its data? Start with: Uniqueness of the Ricci Flow on Complete Noncompact Manifolds (Chen et al., 2005) Boundaries & non-compact Ricci flow beyond closed manifolds: complete non-compact spaces, manifolds with boundary, and asymptotically flat or hyperbolic ends. Start with: Deforming the metric on complete Riemannian manifolds (Shi, 1989)

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.