Abstract:
The Chern-Ricci flow is an evolution equation of Hermitian metrics by their Chern-Ricci form, first introduced by Gill. Building on recent works, we describe explicit solutions to the Chern-Ricci flow for various non-Kähler surfaces. We establish new estimates in the case of finite time non-collapsing, analogous to some known results for the Kähler-Ricci flow. This allows us to show that finite time non-collapsing singularities of the Chern-Ricci flow on compact complex (non-Kähler) manifolds form along analytic subsets, analogous to some known results for the Kähler-Ricci flow, thus partially answering a question of Tosatti-Weinkove.