Ricci solitons, conical singularities, and nonuniqueness
Abstract: In dimension n=3, there is a complete theory of weak solutions of Ricci flow -- the singular Ricci flows introduced by Kleiner and Lott. These are unique across singularities, as was proved by Bamler and Kleiner. In joint work with Angenent, we show that uniqueness should not be expected to hold for Ricci flow weak solutions in dimensions n>4, not even topologically. Specifically, we exhibit a discrete family of asymptotically conical gradient shrinking soliton singularity models, each of which admits non-unique forward continuations by gradient expanding solitons.