Paper · Jun 1, 2025

Rigidity of Five-Dimensional shrinking gradient Ricci solitons

Fengjiang Li, Jianyu Ou, Yuanyuan Qu, Guoqiang Wu

math.DGarXiv:2506.00887
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Abstract

Suppose is a 5-dimensional complete shrinking gradient Ricci soliton with . If it has bounded curvature, we prove that it is a finite quotient of .

Ricci solitonsStability & uniqueness

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 A new complete two-dimensional shrinking gradient Kähler-Ricci soliton (Richard H. Bamler, Charles Cifarelli, Ronan J. Conlon et al., 2022)8Bamler 2022 Some rigidity results on shrinking gradient Ricci soliton (Jianyu Ou, Yuanyuan Qu and Guoqiang Wu, 2024)2Ou 2024 Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature (Fengjiang Li, Jianyu Ou, Yuanyuan Qu et al., 2024)1Li 2024 A note on Rigidity of Shrinking Gradient Ricci Solitons with Constant Scalar Curvature (Chen Wang and Guoqiang Wu, 2026)6Wang 2026 A note on four dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature (Chen Wang and Guoqiang Wu, 2026)4Wang 2026 Rigidity of shrinking gradient ricci soliton with constant scalar curvature (Fengjiang Li, Yuanyuan Qu and Guoqiang Wu, 2026)3Li 2026 Rigidity of Kähler-Ricci Solitons with Constant Scalar Curvature (Matheus Horácio, Wenqi Li, Jianyu Ou et al., 2026)7Horácio 2026 Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set (Fengjiang Li, Wenqi Li, Jianyu Ou et al., 2026)5Li 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature

    Fengjiang Li, Jianyu Ou, Yuanyuan Qu et al. PDF

    Topics Stability & uniqueness, Ricci solitons · Same authors Fengjiang Li, Jianyu Ou, Yuanyuan Qu · Shared terms “five dimensional”, “dimensional shrinking”, “shrinking gradient”

  2. Some rigidity results on shrinking gradient Ricci soliton

    Jianyu Ou, Yuanyuan Qu and Guoqiang Wu PDF

    Topics Stability & uniqueness, Ricci solitons · Same authors Jianyu Ou, Yuanyuan Qu, Guoqiang Wu · Shared terms “shrinking gradient”, “gradient Ricci”, “complete shrinking”

  3. Rigidity of shrinking gradient ricci soliton with constant scalar curvature

    Fengjiang Li, Yuanyuan Qu and Guoqiang Wu PDF

    Topics Stability & uniqueness, Ricci solitons · Same authors Fengjiang Li, Yuanyuan Qu, Guoqiang Wu · Shared terms “shrinking gradient”, “gradient Ricci”, “complete shrinking”

  4. A note on four dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature

    Chen Wang and Guoqiang Wu PDF

    Topics Ricci solitons · Same author Guoqiang Wu · Shared terms “dimensional shrinking”, “shrinking gradient”, “gradient Ricci”

  5. Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set

    Fengjiang Li, Wenqi Li, Jianyu Ou et al. PDF

    Topics Stability & uniqueness, Ricci solitons · Same authors Fengjiang Li, Jianyu Ou, Yuanyuan Qu · Shared terms “shrinking gradient”, “gradient Ricci”

  6. A note on Rigidity of Shrinking Gradient Ricci Solitons with Constant Scalar Curvature

    Chen Wang and Guoqiang Wu PDF

    Topics Stability & uniqueness, Ricci solitons · Same author Guoqiang Wu · Shared terms “shrinking gradient”, “finite quotient”, “gradient Ricci”

  7. Rigidity of Kähler-Ricci Solitons with Constant Scalar Curvature

    Matheus Horácio, Wenqi Li, Jianyu Ou et al. PDF

    Topics Stability & uniqueness, Ricci solitons · Same authors Jianyu Ou, Guoqiang Wu · Shared terms “gradient Ricci”, “quotient”

  8. A new complete two-dimensional shrinking gradient Kähler-Ricci soliton

    Richard H. Bamler, Charles Cifarelli, Ronan J. Conlon et al. PDF

    Topics Ricci solitons · Shared terms “dimensional shrinking”, “shrinking gradient”, “complete shrinking”

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 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) Stability & uniqueness When does a flow started near a special solution stay near it, and when is a flow determined by its data? Start with: Uniqueness of the Ricci Flow on Complete Noncompact Manifolds (Chen et al., 2005)

In the guidebook

  1. 11B.1
    Ricci SolitonsBook 11B · Solitons, Compactness and Singularities

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

  2. 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.