Paper · May 20, 2026

On the Hamilton-Tian Conjecture in a compact transverse Fano Sasakian -manifold

Shu-Cheng Chang, Yingbo Han, Chien Lin, Chin-Tung Wu

math.DGarXiv:2605.20852
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Abstract

In this paper, we first confirm the Hamilton-Tian conjecture for the Sasaki-Ricci flow in a compact transverse Fano quasi-regular Sasakian -manifold with klt foliation singularities. Secondly, we derive the compactness theorem of Sasaki-Ricci solitons on transverse Fano quasi-regular Sasakian -manifolds. Then,by the second Sasakian structure theorem, we confirm the Hamilton-Tian conjecture for a compact transverse Fano Sasakian -manifold. With its applications, we show that the gradient Sasaki-Ricci soliton orbifold metric on a compact Sasakian -manifold is Sasaki-Einstein if is transverse -stable.

Comments: Combining some part of our previous paper arXiv:2210.12702

Ricci flowRicci solitonsSingularitiesKähler geometryLimit spaces & RCDAnalytic minimal model programSasakian & contact geometry

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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 Convergence of the Sasaki-Ricci flow on Sasakian 5-manifolds of general type (Shu-Cheng Chang, Yingbo Han, Chien Lin et al., 2022)1Chang 2022 Foliation divisorial contraction by the Sasaki-Ricci flow on Sasakian 5-manifolds (Shu-Cheng Chang, Chien Lin and Chin-Tung Wu, 2022)2Chang 2022 Gradient Shrinking Sasaki-Ricci Solitons on Sasakian Manifolds of Dimension Up to Seven (Der-Chen Chang, Shu-Cheng Chang, Yingbo Han et al., 2022)3Chang 2022 Legendrian mean curvature flow in η-Einstein Sasakian manifolds (Shu-Cheng Chang, Yingbo Han and Chin-Tung Wu, 2023)8Chang 2023 On the existence of conic Sasaki-Einstein metrics on log Fano Sasakian manifolds of dimension five (Shu-Cheng Chang, Fengjiang Li, Chien Lin et al., 2024)4Chang 2024 Transverse Rigidity of Shrinking Sasaki-Ricci Solitons (Shu-Cheng Chang, Fengjiang Li, Chien Lin et al., 2025)5Chang 2025 Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons (Shu-Cheng Chang, Yingbo Han and Chin-Tung Wu, 2025)6Chang 2025 Gradient Shrinking Sasaki-Ricci Solitons with Harmonic Weyl Tensor (Shu-Cheng Chang and Hongbing Qiu, 2025)7Chang 2025
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 Sasaki-Ricci flow on Sasakian 5-manifolds of general type

    Shu-Cheng Chang, Yingbo Han, Chien Lin et al. PDF

    Topics Analytic minimal model program, Sasakian & contact geometry, Singularities · Same authors Shu-Cheng Chang, Yingbo Han, Chien Lin · Shared terms “Sasaki Ricci”, “transverse”, “regular Sasakian”

  2. Foliation divisorial contraction by the Sasaki-Ricci flow on Sasakian 5-manifolds

    Shu-Cheng Chang, Chien Lin and Chin-Tung Wu PDF

    Topics Analytic minimal model program, Sasakian & contact geometry, Singularities · Same authors Shu-Cheng Chang, Chien Lin, Chin-Tung Wu · Shared terms “Sasaki Ricci”, “foliation singularities”, “regular Sasakian”

  3. Gradient Shrinking Sasaki-Ricci Solitons on Sasakian Manifolds of Dimension Up to Seven

    Der-Chen Chang, Shu-Cheng Chang, Yingbo Han et al. PDF

    Topics Sasakian & contact geometry, Kähler geometry, Singularities · Same authors Shu-Cheng Chang, Yingbo Han, Chien Lin · Shared terms “Sasaki Ricci”, “Fano Sasakian”, “transverse Fano”

  4. On the existence of conic Sasaki-Einstein metrics on log Fano Sasakian manifolds of dimension five

    Shu-Cheng Chang, Fengjiang Li, Chien Lin et al. PDF

    Topics Sasakian & contact geometry, Kähler geometry, Ricci solitons · Same authors Shu-Cheng Chang, Chien Lin, Chin-Tung Wu · Shared terms “Fano Sasakian”, “Sasaki Ricci”, “compact transverse”

  5. Transverse Rigidity of Shrinking Sasaki-Ricci Solitons

    Shu-Cheng Chang, Fengjiang Li, Chien Lin et al. PDF

    Topics Sasakian & contact geometry, Singularities, Ricci solitons · Same authors Shu-Cheng Chang, Chien Lin · Shared terms “Sasaki Ricci”, “transverse”, “Sasaki Einstein”

  6. Geometry and Topology of Gradient Shrinking Sasaki-Ricci Solitons

    Shu-Cheng Chang, Yingbo Han and Chin-Tung Wu PDF

    Topics Sasakian & contact geometry, Kähler geometry, Ricci solitons · Same authors Shu-Cheng Chang, Yingbo Han, Chin-Tung Wu · Shared terms “Sasaki Ricci”, “transverse”, “Secondly”

  7. Gradient Shrinking Sasaki-Ricci Solitons with Harmonic Weyl Tensor

    Shu-Cheng Chang and Hongbing Qiu PDF

    Topics Sasakian & contact geometry, Ricci solitons · Same author Shu-Cheng Chang · Shared terms “Sasaki Ricci”

  8. Legendrian mean curvature flow in -Einstein Sasakian manifolds

    Shu-Cheng Chang, Yingbo Han and Chin-Tung WuWider flows PDF

    Topics Sasakian & contact geometry, Singularities · Same authors Shu-Cheng Chang, Yingbo Han, Chin-Tung Wu · Shared terms “Einstein”

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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) 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) Singularities On a closed manifold the flow usually cannot run forever: curvature blows up in finite time, often because a neck pinches off. Start with: The formations of singularities in the Ricci Flow (Hamilton, 1993) 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

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    Blow-Ups, Blow-Downs and Splitting at InfinityBook 11B · Solitons, Compactness and Singularities

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  2. 11B.6
    Rotationally Symmetric Flows and the Standard SolutionBook 11B · Solitons, Compactness and Singularities

    The neckpinch in equations: warped products under the flow, what the maximum principle forces, and the standard solution that surgery glues in.

  3. 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.