Paper · Sep 10, 2020

Asymptotic curvature estimate for steady solitons

Daoyuan Han

As on arXiv

Abstract

In this note, we shall investigate the asymptotic curvature estimate on steady Ricci solitons.

Submitted
Sep 10, 2020
Subjects
math.DG

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 Yamabe Flow: steady solitons and type II singularities (Beomjun Choi and Panagiota Daskalopoulos, 2017)2Choi 2017 Curvature estimates for steady Ricci solitons (Pak-Yeung Chan, 2019)3Chan 2019 The isoperimetric inequality in steady Ricci solitons (Yuqiao Li, 2019)5Li 2019 Curvature estimates for four-dimensional complete gradient expanding Ricci solitons (Huai-Dong Cao and Tianbo Liu, 2021)4Cao 2021 A comparison theorem for steady Ricci solitons (Benedito Leandro and Jeferson Poveda, 2022)6Leandro 2022 On curvature estimates for four-dimensional gradient Ricci solitons (Huai-Dong Cao, 2025)1Cao 2025 Asymptotic Geometry of Four-Dimensional Steady Solitons (Aprameya Girish Hebbar and Natasa Sesum, 2026)7Hebbar 2026 Steady soliton with 𝓛¹ decay curvature (Ming Hsiao, 2026)8Hsiao 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. On curvature estimates for four-dimensional gradient Ricci solitons

    Huai-Dong Cao

    Topics Ricci solitons · Shared terms “curvature estimates”, “steady Ricci”

  2. Yamabe Flow: steady solitons and type II singularities

    Beomjun Choi and Panagiota Daskalopoulos

    Topics Ricci solitons · Shared terms “steady soliton”

  3. Curvature estimates for steady Ricci solitons

    Pak-Yeung Chan

    Topics Ricci solitons · Shared terms “curvature estimates”, “steady Ricci”

  4. Curvature estimates for four-dimensional complete gradient expanding Ricci solitons

    Huai-Dong Cao and Tianbo Liu

    Topics Ricci solitons · Shared terms “asymptotic curvature”, “curvature estimates”

  5. The isoperimetric inequality in steady Ricci solitons

    Yuqiao Li

    Topics Ricci solitons · Shared terms “steady soliton”, “steady Ricci”

  6. A comparison theorem for steady Ricci solitons

    Benedito Leandro and Jeferson Poveda

    Topics Ricci solitons · Shared terms “steady soliton”, “steady Ricci”

  7. Asymptotic Geometry of Four-Dimensional Steady Solitons

    Aprameya Girish Hebbar and Natasa Sesum

    Topics Ricci solitons · Shared terms “steady soliton”

  8. Steady soliton with decay curvature

    Ming Hsiao

    Topics Ricci solitons · Shared terms “steady soliton”

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.

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.