7 papers
Type I estimates for the Kähler-Ricci flow II
Wangjian Jian, Jian Song
In this paper, we establish geometric consequences of our Type I scalar curvature estimate for finite-time solutions of the Kähler-Ricci flow on compact Kähler manifolds. We prove…
Type I estimates for the Kahler-Ricci flow I
Wangjian Jian, Jian Song
We establish the Type I estimate for the scalar curvature of the Kahler-Ricci flow on compact Kahler manifolds, for arbitrary smooth initial metrics, whenever the flow develops fin…
Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles II
Wangjian Jian, Jian Song
The analytic minimal model program proposed in \cite{SongTianSingularities, JST} seeks to describe the birational transitions and fibre collapsing of the Kähler--Ricci flow through…
Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles
Wangjian Jian, Jian Song
We study collapsing finite-time singularities of the unnormalized Kähler--Ricci flow on Fano bundles arising in the analytic minimal model program. For a Fano bundle $X^n\rightarro…
Finite time singularities of the Kähler-Ricci flow
Wangjian Jian, Jian Song, Gang Tian
We establish the scalar curvature and distance bounds, extending Perelman's work on the Fano Kähler-Ricci flow to general finite time solutions of the Kähler-Ricci flow. These boun…
Geometric regularity of blow-up limits of the Kähler-Ricci flow
Max Hallgren, Wangjian Jian, Jian Song +1
We establish geometric regularity for Type I blow-up limits of the Kähler-Ricci flow based at any sequence of Ricci vertices. As a consequence, the limiting flow is continuous in t…
A new proof of Perelman's scalar curvature and diameter estimates for the Kähler-Ricci flow on Fano manifolds
Wangjian Jian, Jian Song, Gang Tian
In this note, we give a new proof for Perelman's scalar curvature and diameter estimates for the Kähler-Ricci flow on Fano manifolds. The proof relies on a new Harnack estimate for…