Uniqueness of complete noncompact Ricci flows

Determine whether Ricci flows with smooth initial data in the complete noncompact setting are unique in full generality.

Background

The paper studies uniqueness for Ricci flows emerging from singular or nonsmooth initial metric spaces. Although the paper proves uniqueness under scaling-invariant curvature bounds, noncollapsing, sectional-curvature lower bounds, and a uniform Reifenberg condition on the initial space, the broader complete noncompact smooth-initial-data problem is not resolved. The authors identify this as a limitation of the existing theory and obtain only a partial answer in the singular setting.