Ricci Solitons, Conical Singularities, and Nonuniqueness

In dimension $n=3$, there is a complete theory of weak solutions Ricci flow - the singular flows introduced by Kleiner and Lott which are unique across singularities, as was proved Bamler Kleiner. We show that uniqueness should not be expected to hold for in dimensions $n\geq5$. Specifically, we exhibit discrete family asymptotically conical gradient shrinking solitons, each admits non-unique forward continuations expanding solitons. (v2) recast Main Theorem language Lott's Flow spacetimes addition topological nonuniqueness possible construct.