Paper · Sep 27, 2025

Two Comments on "Laplace comparison on Kahler Ricci flow and convergence (arXiv:2509.14820v1)"

Xiuxiong Chen, Bing Wang

math.DGarXiv:2509.23346v2
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Abstract

We clarify the definition of polarized canonical radius in the study of Kahler Ricci flow.

Comments: Comment on arXiv:2509.14820

Ricci flowKähler–Ricci flowKähler geometry

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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 2021, 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 modified Kähler-Ricci flow, II (Haotian Wu and Zhou Zhang, 2022)3Wu 2022 Quantization of the Kähler-Ricci flow and optimal destabilizer for a Fano manifold (Tomoyuki Hisamoto, 2024)2Hisamoto 2024 Immortal solutions of the Kähler-Ricci flow (Valentino Tosatti, 2024)6Tosatti 2024 Laplace comparison on Kähler Ricci flow and convergence (Gang Tian, Qi S. Zhang, Zhenlei Zhang et al., 2025)1Tian 2025 Weak transcendental base-point freeness and diameter lower bounds for the Kähler-Ricci flow (Junsheng Zhang, 2025)7Zhang 2025 Kähler-Ricci Flow: from divisors to cusps (Eleonora Di Nezza, Vincent Guedj and Chinh H. Lu, 2026)8Di Nezza 2026 Geometric smoothing by the Kähler-Ricci Flow (Eleonora Di Nezza, Vincent Guedj and Chinh Hoang Lu, 2026)4Di Nezza 2026 Kähler-Ricci Flow is Symplectic Deflation plus an Exact Symplectic Deformation (Randall R. Van Why, 2026)5Van Why 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Laplace comparison on Kähler Ricci flow and convergence

    Gang Tian, Qi S. Zhang, Zhenlei Zhang et al. PDF

    Topics Kähler–Ricci flow, Kähler geometry · Shared terms “Laplace comparison”

  2. Quantization of the Kähler-Ricci flow and optimal destabilizer for a Fano manifold

    Tomoyuki Hisamoto PDF

    Topics Kähler–Ricci flow, Kähler geometry

  3. The modified Kähler-Ricci flow, II

    Haotian Wu and Zhou Zhang PDF

    Topics Kähler–Ricci flow, Kähler geometry

  4. Geometric smoothing by the Kähler-Ricci Flow

    Eleonora Di Nezza, Vincent Guedj and Chinh Hoang Lu PDF

    Topics Kähler–Ricci flow, Kähler geometry

  5. Kähler-Ricci Flow is Symplectic Deflation plus an Exact Symplectic Deformation

    Randall R. Van Why PDF

    Topics Kähler–Ricci flow, Kähler geometry

  6. Immortal solutions of the Kähler-Ricci flow

    Valentino Tosatti PDF

    Topics Kähler–Ricci flow, Kähler geometry

  7. Weak transcendental base-point freeness and diameter lower bounds for the Kähler-Ricci flow

    Junsheng Zhang PDF

    Topics Kähler–Ricci flow, Kähler geometry

  8. Kähler-Ricci Flow: from divisors to cusps

    Eleonora Di Nezza, Vincent Guedj and Chinh H. Lu PDF

    Topics Kähler–Ricci flow, Kähler geometry

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.

Ricci flow Hamilton's Ricci flow evolves a Riemannian metric by minus twice its Ricci curvature. It is a nonlinear heat equation for geometry: it spreads… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Kähler–Ricci flow Ricci flow started from a Kähler metric stays Kähler and reduces to a single scalar equation, a parabolic complex Monge–Ampère equation. Start with: Deformation of Kähler matrics to Kähler-Einstein metrics on compact Kähler manifolds (Cao, 1985) Kähler geometry Complex manifolds with compatible Riemannian metrics. Here Ricci curvature is the complex Hessian of a log-determinant, so Ricci flow becomes a… Start with: On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I (Yau, 1978)

In the guidebook

  1. 5A.6
    Where This Track LeadsBook 5A · Complex Analysis and Conformal Geometry

    The Kähler–Ricci flow, and when to come back to it.

  2. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.

  3. 10A.12
    Curve Shortening and Minimal DiscsBook 10A · Three-Manifolds and Geometrization

    How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.