Regularity of the Kähler-Ricci flow

In this short note, we announce a regularity theorem for the Kähler-Ricci flow on a compact Fano manifold (Kähler manifold with positive first Chern class) and its application to the limiting behavior of the Kähler-Ricci flow on Fano 3-manifolds. Moreover, we also present a partial C⁰ estimate of the Kähler-Ricci flow under the regularity assumption, which extends previous works on Kähler-Einstein metrics and shrinking Kähler-Ricci solitons. The detailed proof will appear elsewhere.