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OP-11441Status unassessedGeometry and topology

Expanding Solitons from Divisorial Contractions

PDE methods in complex geometry · AIMPL workshop record

MSC 32 · Several complex variables and analytic spaces

Editorial mapping of AIMPL list topic: PDE methods in complex geometry. http://aimpl.org/pdecomplexgeom/ Not an author-supplied MSC code.

Workshop record · status unassessedAs of 2026-09-10 source snapshot; not a current-status certificationSource & evidence ↓
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Problem statement

Consider a Kahler-Ricci Flow (M2,(gt)t∈[0,T))(M^{2},(g_{t})_{t\in[0,T)}) developing a finite-time singularity with lim⁡t→TVolωt(M)>0\lim_{t\to T}\text{Vol}_{\omega_{t}}(M)>0. Doing a Type-I blowup backwards in time, is the flow coming out of the singularity Cao's expanding soliton?

In the Riemannian case, one can flow out of isolated cone singularities with positive curvature operator. Can one do this in the Kahler setting instead assuming the cones have nonnegative holomorphic bisectional curvature.

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Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.

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References
  1. [1]PDE methods in complex geometry · Original question link
  2. [2]AIMPL source bibliography link
  3. [3]AIMPL text license · CC BY-SA 3.0 linkAIM Problem Lists (AIMPL), original contributors; CC BY-SA 3.0. Adaptation: structural TeX converted to Markdown, documented source macros expanded, and source bibliography links added. Mathematical wording retained. These adapted source texts remain under CC BY-SA 3.0.

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