Paper · Mar 21, 2019

Curvature growth of some 4-dimensional gradient Ricci soliton singularity models

Bennett Chow, Michael Freedman, Henry Shin, Yongjia Zhang

As on arXiv

Abstract

In this note we discuss estimates for the curvature of 4-dimensional gradient Ricci soliton singularity models by applying Perelman's point selection, a fundamental result of Cheeger and Naber, and topological lemmas.

Submitted
Mar 21, 2019
Last revised
Mar 26, 2021 (v2)
Subjects
math.DG, math.AT
Journal
Advances in Mathematics Advances in Mathematics, Volume 372, 7 October 2020, 107303
DOI
10.1016/j.aim.2020.107303

Comments: Revised version, as appeared in Advances in Mathematics 372 (2020), article number 107303. We would like to thank the referee for their suggestions

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 2016, 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 On the classification of four-dimensional gradient Ricci solitons (Fei Yang and Liangdi Zhang, 2017)5Yang 2017 On Four-dimensional Steady gradient Ricci solitons that dimension reduce (Bennett Chow, Yuxing Deng and Zilu Ma, 2020)4Chow 2020 Four-Dimensional Steady Gradient Ricci Solitons with 3-Cylindrical Tangent Flows at Infinity (Richard Bamler, Bennett Chow, Yuxing Deng et al., 2021)2Bamler 2021 Hamilton-Ivey estimates for gradient Ricci solitons (Pak-Yeung Chan, Zilu Ma and Yongjia Zhang, 2021)7Chan 2021 Lower bounds for the scalar curvatures of Ricci flow singularity models (Pak-Yeung Chan, Bennett Chow, Zilu Ma et al., 2022)3Chan 2022 Dimension Reduction for Positively Curved Steady Solitons (Pak-Yeung Chan, Zilu Ma and Yongjia Zhang, 2023)8Chan 2023 Correction to: Curvature growth of some 4-dimensional gradient Ricci soliton singularity models (Bennett Chow, Michael H. Freedman, Henry Shin et al., 2025)1Chow 2025 On curvature estimates for four-dimensional gradient Ricci solitons (Huai-Dong Cao, 2025)6Cao 2025
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Correction to: Curvature growth of some 4-dimensional gradient Ricci soliton singularity models

    Bennett Chow, Michael H. Freedman, Henry Shin et al.

    Topics 4-manifolds, Singularities, Ricci solitons · Same authors Bennett Chow, Michael Freedman, Henry Shin · Shared terms “curvature growth”, “dimensional gradient”, “singularity models”

  2. Four-Dimensional Steady Gradient Ricci Solitons with -Cylindrical Tangent Flows at Infinity

    Richard Bamler, Bennett Chow, Yuxing Deng et al.

    Topics 4-manifolds, Singularities, Ricci solitons · Same authors Bennett Chow, Yongjia Zhang · Shared terms “singularity models”, “gradient Ricci”

  3. Lower bounds for the scalar curvatures of Ricci flow singularity models

    Pak-Yeung Chan, Bennett Chow, Zilu Ma et al.

    Topics Singularities, Ricci solitons · Same authors Bennett Chow, Yongjia Zhang · Shared terms “singularity models”, “Cheeger”

  4. On Four-dimensional Steady gradient Ricci solitons that dimension reduce

    Bennett Chow, Yuxing Deng and Zilu Ma

    Topics 4-manifolds, Singularities, Ricci solitons · Same author Bennett Chow · Shared terms “singularity models”, “gradient Ricci”

  5. On the classification of four-dimensional gradient Ricci solitons

    Fei Yang and Liangdi Zhang

    Topics 4-manifolds, Ricci solitons · Shared terms “dimensional gradient”, “gradient Ricci”

  6. On curvature estimates for four-dimensional gradient Ricci solitons

    Huai-Dong Cao

    Topics 4-manifolds, Ricci solitons · Shared terms “dimensional gradient”, “gradient Ricci”

  7. Hamilton-Ivey estimates for gradient Ricci solitons

    Pak-Yeung Chan, Zilu Ma and Yongjia Zhang

    Topics Singularities, Ricci solitons · Same author Yongjia Zhang · Shared terms “dimensional gradient”, “gradient Ricci”, “singularity models”

  8. Dimension Reduction for Positively Curved Steady Solitons

    Pak-Yeung Chan, Zilu Ma and Yongjia Zhang

    Topics 4-manifolds, Singularities, Ricci solitons · Same author Yongjia Zhang · Shared terms “gradient Ricci”

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In the guidebook

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