Paper · Jun 7, 2026

Asymptotic Profiles and Non-Trivial Breathers in Kahler-Ricci Flow

Longteng Chen

math.DGarXiv:2606.08837
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Abstract

In this paper, we investigate the relationship between the long time behaviour of solutions to the Kahler-Ricci flow on an asymptotically conical gradient Kahler-Ricci expander and the asymptotic behaviour of their initial data at spatial infinity.

Comments: 28 pages, 1 figure, all comments are welcome!

Ricci flowKähler–Ricci flowRicci solitonsKähler geometryBoundaries & non-compactLong-time existence & convergence

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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 Nontrivial breathers for Ricci flow (Peter M. Topping, 2021)6Topping 2021 The modified Kähler-Ricci flow, II (Haotian Wu and Zhou Zhang, 2022)8Wu 2022 Immortal solutions of the Kähler-Ricci flow (Valentino Tosatti, 2024)5Tosatti 2024 Global Ricci Curvature Behaviour for the Kähler-Ricci Flow with Finite Time Singularities (Alexander Bednarek, 2024)7Bednarek 2024 Uniqueness of asymptotically conical Kähler-Ricci flow (Longteng Chen, 2025)2Chen 2025 Stability of asymptotically conical gradient Kähler-Ricci expanders (Longteng Chen, 2025)1Chen 2025 Expanding Soliton Models for Kähler-Ricci Flow Near Conical Singularities (Longteng Chen, Max Hallgren and Lucas Lavoyer, 2026)3Chen 2026 Kähler-Ricci Tangent Flows in the Analytic Minimal Model Program (Longteng Chen, Max Hallgren and Lucas Lavoyer, 2026)4Chen 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Stability of asymptotically conical gradient Kähler-Ricci expanders

    Longteng Chen PDF

    Topics Kähler–Ricci flow, Long-time existence & convergence, Boundaries & non-compact · Same author Longteng Chen · Shared terms “conical gradient”, “Ricci expander”, “spatial infinity”

  2. Uniqueness of asymptotically conical Kähler-Ricci flow

    Longteng Chen PDF

    Topics Kähler–Ricci flow, Boundaries & non-compact, Kähler geometry · Same author Longteng Chen · Shared terms “asymptotically conical”

  3. Expanding Soliton Models for Kähler-Ricci Flow Near Conical Singularities

    Longteng Chen, Max Hallgren and Lucas Lavoyer PDF

    Topics Kähler–Ricci flow, Kähler geometry, Ricci solitons · Same author Longteng Chen · Shared terms “Ricci expander”, “initial data”

  4. Kähler-Ricci Tangent Flows in the Analytic Minimal Model Program

    Longteng Chen, Max Hallgren and Lucas Lavoyer PDF

    Topics Kähler–Ricci flow, Boundaries & non-compact, Kähler geometry · Same author Longteng Chen · Shared terms “asymptotically conical”, “expander”

  5. Immortal solutions of the Kähler-Ricci flow

    Valentino Tosatti PDF

    Topics Kähler–Ricci flow, Long-time existence & convergence, Kähler geometry

  6. Nontrivial breathers for Ricci flow

    Peter M. Topping PDF

    Topics Boundaries & non-compact · Shared terms “breather”

  7. Global Ricci Curvature Behaviour for the Kähler-Ricci Flow with Finite Time Singularities

    Alexander Bednarek PDF

    Topics Kähler–Ricci flow, Kähler geometry

  8. The modified Kähler-Ricci flow, II

    Haotian Wu and Zhou Zhang 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) Ricci solitons Metrics that change under Ricci flow only by scaling and diffeomorphisms: shrinking, steady or expanding solitons. Start with: The Ricci flow on surfaces (Hamilton, 1988) 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. 11B.1
    Ricci SolitonsBook 11B · Solitons, Compactness and Singularities

    Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

  3. 12B.2
    The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery

    Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.