An orbifold cylinder is a cylindrical Ricci-flow soliton with orbifold singularities. An ancient Ricci flow is a Ricci flow defined on a time interval extending to -∞. Orbifold-cylinder conjecture. There exist ancient Ricci flows from orbifold cylinders. This is motivated by the authors' construction of ancient Ricci flows from spherical orbifolds and is presented as an open direction concerning Ricci-flow singularity formation.

The conjecture on ancient Ricci flows from orbifold cylinders

The conjecture is explicitly posed in a 2024 paper, which asks whether ancient Ricci flows can arise from orbifold cylinders. The paper treats this as an open direction motivated by constructions from spherical, hyperbolic, and complex-hyperbolic Einstein orbifolds.

Known results

The 2024 paper constructs ancient and immortal Ricci flows from Einstein orbifolds using bubbling of Ricci-flat ALE metrics.
It gives evidence that singular spherical and cylindrical orbifolds should not occur as finite-time singularity models, but this is not proved and does not settle the existence conjecture.
Related 2024 work classifies certain ancient spin ALE flows with tangent model $\mathbb{R}^{4}/\Gamma$ , not flows from orbifold cylinders.

Current status (as of August 2026): The conjecture remains open; no verified proof, disproof, or claimed resolution was found.

The conjecture on ancient Ricci flows from orbifold cylinders

Primary source

Progress summary

Solutions 0