Paper · Dec 12, 2025

Pluriclosed flow on Oeljeklaus-Toma manifolds

Jeffrey Streets, Xiaokang Wang

math.DGarXiv:2512.11246
PDF Abstract page

As on arXiv

Abstract

We establish global existence of the pluriclosed flow with arbitrary initial data on Oeljeklaus-Toma manifolds, and Gromov-Hausdorff convergence of blowdown limits to a torus under natural conjectural bounds on the flow at infinity. In the case of generalized Kähler-Ricci flow we prove refined a priori estimates in support of these conjectural bounds.

Comments: The authors warmly dedicate this article to Professor Gang Tian on the occasion of his 65th birthday. Comments welcome!

Ricci flowKähler–Ricci flowGeneralized & G₂ flowsKähler geometryLimit spaces & RCDLong-time existence & convergence

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 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 Four-dimensional generalized Ricci flows with nilpotent symmetry (Steven Gindi and Jeffrey Streets, 2021)7Gindi 2021 The generalized Kähler Calabi-Yau problem (Vestislav Apostolov, Xin Fu, Jeffrey Streets et al., 2022)1Apostolov 2022 Optimal Transport and Generalized Ricci Flow (Eva Kopfer and Jeffrey Streets, 2023)6Kopfer 2023 Derivative estimates of pluriclosed flow (Yanan Ye, 2023)5Ye 2023 Pluriclosed flow and the Hull-Strominger system (Mario Garcia-Fernandez, Raul Gonzalez Molina and Jeffrey Streets, 2024)2Garcia-Ferna 2024 Chern-Ricci flow and t-Gauduchon Ricci-flat condition (Eder M. Correa, Giovane Galindo and Lino Grama, 2025)3Correa 2025 Dynamical stability of Pluriclosed and Generalized Ricci solitons (Kuan-Hui Lee, 2025)8Lee 2025 Long-Time Behavior of the α-Ricci Flow on the 2-Torus (Yifan Guo and Xiaokang Wang, 2026)4Guo 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. The generalized Kähler Calabi-Yau problem

    Vestislav Apostolov, Xin Fu, Jeffrey Streets et al. PDF

    Topics Generalized & G₂ flows, Kähler–Ricci flow, Long-time existence & convergence · Same author Jeffrey Streets · Shared terms “global existence”, “priori estimates”, “initial data”

  2. Pluriclosed flow and the Hull-Strominger system

    Mario Garcia-Fernandez, Raul Gonzalez Molina and Jeffrey Streets PDF

    Topics Generalized & G₂ flows, Long-time existence & convergence, Kähler geometry · Same author Jeffrey Streets · Shared terms “pluriclosed flow”, “conjectural”, “priori estimates”

  3. Chern-Ricci flow and t-Gauduchon Ricci-flat condition

    Eder M. Correa, Giovane Galindo and Lino Grama PDF

    Topics Generalized & G₂ flows, Limit spaces & RCD, Kähler geometry · Shared terms “pluriclosed flow”, “Gromov Hausdorff”

  4. Long-Time Behavior of the -Ricci Flow on the 2-Torus

    Yifan Guo and Xiaokang Wang PDF

    Topics Limit spaces & RCD, Long-time existence & convergence · Same author Xiaokang Wang · Shared terms “global existence”, “Hausdorff”, “Gromov”

  5. Derivative estimates of pluriclosed flow

    Yanan Ye PDF

    Topics Generalized & G₂ flows, Kähler geometry · Shared terms “pluriclosed flow”

  6. Optimal Transport and Generalized Ricci Flow

    Eva Kopfer and Jeffrey Streets PDF

    Topics Generalized & G₂ flows, Limit spaces & RCD · Same author Jeffrey Streets

  7. Four-dimensional generalized Ricci flows with nilpotent symmetry

    Steven Gindi and Jeffrey Streets PDF

    Topics Generalized & G₂ flows, Long-time existence & convergence · Same author Jeffrey Streets · Shared terms “blowdown limits”

  8. Dynamical stability of Pluriclosed and Generalized Ricci solitons

    Kuan-Hui Lee PDF

    Topics Generalized & G₂ flows · Shared terms “pluriclosed”

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) Generalized & G₂ flows Ricci-type flows for geometry beyond Kähler metrics. Generalized Ricci flow couples a metric to a closed 3-form, pluriclosed and Chern–Ricci flows… Start with: A parabolic flow of pluriclosed metrics (Streets et al., 2009) 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. 6C.11
    Optimal Transport and Ricci CurvatureBook 6C · Nonlinear PDE: Variational and Geometric Methods

    Kantorovich duality, Wasserstein geometry, the heat equation as a gradient flow of entropy, displacement convexity, and Ricci curvature as convexity, from Lott–Sturm–Villani to McCann–Topping and the reduced volume.

  3. 9B.4
    Convergence of ManifoldsBook 9B · Comparison, Convergence and Heat on Manifolds

    Gromov–Hausdorff and Cheeger–Gromov convergence, and the compactness theorem.