Paper · Nov 7, 2024

The asymptotic behavior of the steady gradient Kähler-Ricci soliton of the Taub-NUT type of Apostolov and Cifarelli

Daheng Min

As on arXiv

Abstract

We first determine the asymptotic cone of the steady gradient Kähler-Ricci soliton of the Taub-NUT type constructed by Apostolov and Cifarell. Then we study a special case and prove that it is an ALF Calabi-Yau metric in a certain sense. Finally we construct new ALF Calabi-Yau metrics on crepant resolution of its quotients modeled on it using the method of Tian-Yau-Hein.

Submitted
Nov 7, 2024
Subjects
math.DG

Comments: 38 pages

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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 Hamiltonian 2-forms and new explicit Calabi–Yau metrics and gradient steady Kähler–Ricci solitons on ℂⁿ (Vestislav Apostolov and Charles Cifarelli, 2023)1Apostolov 2023 A family of Kähler flying wing steady Ricci solitons (Pak-Yeung Chan, Ronan J. Conlon and Yi Lai, 2024)8Chan 2024 Explicit complete Ricci-flat metrics and Kähler-Ricci solitons on direct sum bundles (Charles Cifarelli, 2024)3Cifarelli 2024 From Kähler Ricci solitons to Calabi-Yau Kähler cones (Vestislav Apostolov, Abdellah Lahdili and Eveline Legendre, 2024)2Apostolov 2024 Uniqueness of asymptotically conical shrinking gradient Kähler-Ricci solitons (Carlos Esparza, 2025)4Esparza 2025 Uniqueness of shrinking Kähler-Ricci solitons on resolutions of Kähler cones (Ronan J. Conlon and Alix Deruelle, 2026)6Conlon 2026 L^p Liouville theorems for pluriharmonic functions on gradient Kähler-Ricci solitons (Guangwen Zhao, 2026)7Zhao 2026 Uniqueness of the soliton vector field of a shrinking gradient Kähler-Ricci soliton (Ronan J. Conlon and Alix Deruelle, 2026)5Conlon 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Hamiltonian -forms and new explicit Calabi–Yau metrics and gradient steady Kähler–Ricci solitons on

    Vestislav Apostolov and Charles Cifarelli

    Topics Ricci-flat & Calabi–Yau, Kähler–Ricci solitons, Kähler geometry · Shared terms “Taub NUT”, “Yau metrics”

  2. From Kähler Ricci solitons to Calabi-Yau Kähler cones

    Vestislav Apostolov, Abdellah Lahdili and Eveline Legendre

    Topics Ricci-flat & Calabi–Yau, Kähler–Ricci solitons, Kähler geometry

  3. Explicit complete Ricci-flat metrics and Kähler-Ricci solitons on direct sum bundles

    Charles Cifarelli

    Topics Ricci-flat & Calabi–Yau, Kähler–Ricci solitons, Kähler geometry · Shared terms “Yau metrics”, “Apostolov”, “ALF”

  4. Uniqueness of asymptotically conical shrinking gradient Kähler-Ricci solitons

    Carlos Esparza

    Topics Ricci-flat & Calabi–Yau, Kähler–Ricci solitons, Kähler geometry · Shared terms “gradient Kähler”, “Yau metrics”

  5. Uniqueness of the soliton vector field of a shrinking gradient Kähler-Ricci soliton

    Ronan J. Conlon and Alix Deruelle

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Shared terms “gradient Kähler”

  6. Uniqueness of shrinking Kähler-Ricci solitons on resolutions of Kähler cones

    Ronan J. Conlon and Alix Deruelle

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Shared terms “gradient Kähler”, “resolution”

  7. Liouville theorems for pluriharmonic functions on gradient Kähler-Ricci solitons

    Guangwen Zhao

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Shared terms “gradient Kähler”

  8. A family of Kähler flying wing steady Ricci solitons

    Pak-Yeung Chan, Ronan J. Conlon and Yi Lai

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Shared terms “gradient Kähler”, “steady gradient”, “Cifarelli”

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.