The higher-dimensional conjecture on Ricci flows with Calabi bubbles

Let $n$ be an integer with $2n\geq 6$. A Calabi metric is the Ricci-flat ALE metric used in the higher-dimensional desingularization construction.

Higher-dimensional Calabi-bubble conjecture. In any dimension $2n\geq 6$, there exist:

• an ancient Ricci flow from a $\mathbb{Z}_n$ quotient of $\mathbb{S}^{2n}$;
• immortal Ricci flows from hyperbolic orbifolds with $\mathbb{R}^{2n}/\mathbb{Z}_n$ singularities.

In both situations, Calabi metrics are bubbled off.

The conjecture proposes that the four-dimensional constructions extend to higher-dimensional orbifold singularities, where the authors expect the obstruction analysis to be simpler.