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On K\"ahler Ricci shrinker surfaces

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arxiv 2301.09784 v2 pith:XRCJJKVI submitted 2023-01-24 math.DG

Yu Li , Bing Wang This is my paper · ORCID
classification math.DG
keywords ahlerriccishrinkersurfacesauthorsboundedclassificationcombining
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In this paper, we prove that any K\"ahler Ricci shrinker surface has bounded sectional curvature. Combining this estimate with earlier work by many authors, we provide a complete classification of all K\"ahler Ricci shrinker surfaces.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Uniqueness of shrinking K\"ahler-Ricci solitons on resolutions of K\"ahler cones

    math.DG 2026-07 conditional novelty 7.0 of 10

    Every complete shrinking gradient Kähler-Ricci soliton on a resolution of a Kähler cone is asymptotically conical, which yields uniqueness up to pullback by biholomorphism.

  2. On the structure of noncollapsed Ricci flow limit spaces

    math.DG 2025-10 unverdicted novelty 7.0 of 10

    Ricci flow limit spaces under bounded entropy have regular parts that form Ricci flow spacetimes and singular sets of codimension at least four.

  3. Gradient Shrinking Ricci Solitons and Modified Sectional Curvature

    math.DG 2025-09 conditional novelty 6.0 of 10

    Under sharp pinching conditions on the self-dual Weyl tensor, scalar curvature, and modified sectional curvature, four-dimensional gradient shrinking Ricci solitons are forced to be locally Kähler, isometric to S^4 or...

  4. Non-collapsing of Ricci shrinkers with bounded curvature

    math.DG 2024-12 conditional novelty 6.0 of 10

    Simply connected Ricci shrinkers with curvature bound |Rm| <= A and finite second homotopy group satisfy mu(g) >= -C(n,A), so unit balls around basepoints have uniformly bounded below volume.

  5. Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature

    math.DG 2024-11 conditional novelty 6.0 of 10

    Every complete noncompact 5D gradient shrinking Ricci soliton with constant scalar curvature R=3λ splits as R²×S³ up to finite quotient.

  6. Cooperative Face Liveness Detection from Optical Flow

    cs.CV 2025-08 unverdicted novelty 5.0 of 10

    A face-liveness method is claimed, but the manuscript body is an unrelated math paper, leaving the claim unsupported and unverifiable.

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