Paper · Oct 11, 2026

A note on the Chern-Yamabe flow on compact Hermitian manifolds with negative Gauduchon degree

Weike Yu

math.DGWider flowsarXiv:2610.15326
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Abstract

In this note, we prove that on a compact Hermitian manifold with negative Gauduchon degree, the Chern-Yamabe flow introduced in our recent work [13] converges to the solution of prescribed Chern scalar curvature problem, provided that the candidate curvature function is nonpositive and not identically zero.

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Submitted
Oct 11, 2026
Subjects
math.DG

Comments: 11 pages

Yamabe flowScalar curvature

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Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Prescribed Chern scalar curvature flow on compact Hermitian manifolds with negative Gauduchon degree

    Weike YuWider flows

    Topics Scalar curvature · Same author Weike Yu · Shared terms “Gauduchon degree”, “negative Gauduchon”, “compact Hermitian”

  2. Generalized Yamabe Flows

    Jørgen Olsen Lye, Boris Vertman and Mannaim Gennaro VittiWider flows

    Topics Yamabe flow, Scalar curvature

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

    Gilles Carron, Eric Chen and Yi WangWider flows

    Topics Yamabe flow · Shared terms “nonpositive”

  4. Convergence of the Weighted Yamabe Flow

    Zetian YanWider flows

    Topics Yamabe flow, Scalar curvature

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

    Claudio Afeltra, Andrea Pinamonti and Pak Tung HoWider flows

    Topics Yamabe flow

  6. Infinite-time incompleteness of noncompact Yamabe flow

    Jin Takahashi and Hikaru YamamotoWider flows

    Topics Yamabe flow

  7. Convergence rate of the weighted Yamabe flow

    Pak Tung Ho, Jinwoo Shin and Zetian YanWider flows

    Topics Yamabe flow

  8. Combinatorial Yamabe flow on hyperbolic bordered surfaces

    Shengyu Li, Xu Xu and Ze ZhouWider 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 within its conformal class, driven by scalar curvature. It is a parabolic approach to the Yamabe problem: find a… Start with: The yamabe flow on locally conformally flat manifolds with positive ricci curvature (Chow, 1992) 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

  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.

  2. 9B.6
    Scalar Curvature and TopologyBook 9B · Comparison, Convergence and Heat on Manifolds

    Positive scalar curvature, its obstructions, and the positive mass theorem.