Tangent flows of Kähler metric flows

Abstract

Abstract We improve the description of 𝔽-limits of noncollapsed Ricci flows in the Kähler setting. In particular, the singular strata S k \mathcal{S}^{k} of such metric flows satisfy S 2 ⁢ j = S 2 ⁢ j + 1 \mathcal{S}^{2j}=\mathcal{S}^{2j+1} . We also prove an analogous result for quantitative strata and show that any tangent flow admits a one-parameter action by isometries, which is locally free on the cone link in the static case. The main results are established using parabolic regularizations of conjugate heat kernel potential functions based at almost-selfsimilar points, which may be of independent interest.