Paper · Mar 26, 2026

A non-Kähler expanding Ricci soliton with a Kähler tangent cone at infinity

Richard H. Bamler, Eric Chen, Ronan J. Conlon

math.DGarXiv:2603.25082
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Abstract

We construct an example of an asymptotically conical (AC) non-Kähler expanding gradient Ricci soliton that has a Kähler tangent cone at infinity. This yields an example of a Kähler cone that can be desingularised by a smooth AC expanding gradient Ricci soliton but not by a smooth AC expanding gradient Kähler–Ricci soliton.

Comments: 10 pages, comments welcome

Ricci solitonsKähler–Ricci solitonsKähler geometryBoundaries & non-compact

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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 On finite time Type I singularities of the Kähler-Ricci flow on compact Kähler surfaces (Charles Cifarelli, Ronan J. Conlon and Alix Deruelle, 2022)8Cifarelli 2022 A new complete two-dimensional shrinking gradient Kähler-Ricci soliton (Richard H. Bamler, Charles Cifarelli, Ronan J. Conlon et al., 2022)2Bamler 2022 Kähler-Ricci Tangent Flows are Infinitesimally Algebraic (Max Hallgren, 2023)6Hallgren 2023 Uniqueness of asymptotically conical Kähler-Ricci flow (Longteng Chen, 2025)7Chen 2025 An Aubin continuity path for asymptotically conical toric shrinking gradient Kähler-Ricci solitons: openness and a solution for t=0 (Ivin Babu, Ronan J. Conlon and Alix Deruelle, 2025)3Babu 2025 Uniqueness of shrinking Kähler-Ricci solitons on resolutions of Kähler cones (Ronan J. Conlon and Alix Deruelle, 2026)1Conlon 2026 Linear Stability of Steady and Expanding Kähler-Ricci Solitons (Lucas Lavoyer and Adam Thompson, 2026)4Lavoyer 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. Uniqueness of shrinking Kähler-Ricci solitons on resolutions of Kähler cones

    Ronan J. Conlon and Alix Deruelle PDF

    Topics Kähler–Ricci solitons, Boundaries & non-compact, Kähler geometry · Same author Ronan J. Conlon · Shared terms “Kähler cone”, “gradient Kähler”, “asymptotically conical”

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

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

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Same authors Richard H. Bamler, Ronan J. Conlon · Shared terms “gradient Kähler”

  3. An Aubin continuity path for asymptotically conical toric shrinking gradient Kähler-Ricci solitons: openness and a solution for

    Ivin Babu, Ronan J. Conlon and Alix Deruelle PDF

    Topics Kähler–Ricci solitons, Boundaries & non-compact, Kähler geometry · Same author Ronan J. Conlon · Shared terms “gradient Kähler”, “asymptotically conical”, “Kähler cone”

  4. Linear Stability of Steady and Expanding Kähler-Ricci Solitons

    Lucas Lavoyer and Adam Thompson PDF

    Topics Kähler–Ricci solitons, Boundaries & non-compact, Kähler geometry · Shared terms “expanding gradient”, “gradient Kähler”, “asymptotically conical”

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

    Ronan J. Conlon and Alix Deruelle PDF

    Topics Kähler–Ricci solitons, Kähler geometry, Ricci solitons · Same author Ronan J. Conlon · Shared terms “gradient Kähler”

  6. Kähler-Ricci Tangent Flows are Infinitesimally Algebraic

    Max Hallgren PDF

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

  7. Uniqueness of asymptotically conical Kähler-Ricci flow

    Longteng Chen PDF

    Topics Kähler–Ricci solitons, Boundaries & non-compact, Kähler geometry · Shared terms “tangent cone”, “Kähler cone”, “asymptotically conical”

  8. On finite time Type I singularities of the Kähler-Ricci flow on compact Kähler surfaces

    Charles Cifarelli, Ronan J. Conlon and Alix Deruelle PDF

    Topics Kähler–Ricci solitons, Boundaries & non-compact, Kähler geometry · Same author Ronan J. Conlon · Shared terms “gradient Kähler”

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) Kähler–Ricci solitons Kähler metrics whose Ricci form differs from the metric by a Lie derivative along a holomorphic vector field. Start with: Uniqueness of Kähler-Ricci solitons (Tian et al., 2000) 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) Boundaries & non-compact Ricci flow beyond closed manifolds: complete non-compact spaces, manifolds with boundary, and asymptotically flat or hyperbolic ends. Start with: Deforming the metric on complete Riemannian manifolds (Shi, 1989)

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.