11 citations · 26 across the 13 of their papers we have counts for
17 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…
CscK metrics near the canonical class
Bin Guo, Wangjian Jian, Yalong Shi +1
Let be a Kähler manifold with semi-ample canonical bundle . It is proved by Jian-Shi-Song that for any Kähler class , there exists such that for all …
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…
estimates for Kähler-Ricci flow on Kähler-Einstein Fano manifolds: a new derivation
Wangjian Jian, Yalong Shi
Assuming Perelman's estimates, we give a new proof of uniform estimate along normalized Kähler-Ricci flow on Fano manifolds with Kähler-Einstein metrics, using Chen-Chen…
Tangent Flows of Kähler Metric Flows
Max Hallgren, Wangjian Jian
We improve the description of -limits of noncollapsed Ricci flows in the Kähler setting. In particular, the singular strata of such metric flows satisfy…
On the improved no-local-collapsing theorem of Ricci flow
Wangjian Jian
In this note we derive an improved no-local-collapsing theorem of Ricci flow under the scalar curvature bound condition along the worldline of the basepoint. It is a refinement of…
Diameter and Ricci curvature estimates for long-time solutions of the Kahler-Ricci flow
Wangjian Jian, Jian Song
It is well known that the Kähler-Ricci flow on a Kähler manifold admits a long-time solution if and only if is a minimal model, i.e., the canonical line bundle is nef…
Global -regularity for 4-dimensional Ricci flow with integral scalar curvature bound
Wangjian Jian
Ge-Jiang (Geom Funct Anal 27:1231-1256, 2017) proved global -regularity for 4-dimensional Ricci flow with bounded scalar curvature. In this note, we extend this result…
Global higher order estimates for collapsing Calabi-Yau metrics on elliptic K3 surfaces
Wangjian Jian, Yalong Shi
We improve Gross-Wilson's local estimates to global ones. As an application, we study the blow-up limits of the degenerating Calabi-Yau metrics on singular fibers.
A "boundedness implies convergence" principle and its applications to collapsing estimates in Kähler geometry
Wangjian Jian, Yalong Shi
We establish a general "boundedness implies convergence" principle for a family of evolving Riemannian metrics. We then apply this principle to collapsing Calabi-Yau metrics and no…
Convergence of scalar curvature of Kahler-Ricci flow on manifolds of positive Kodaira dimension
Wangjian Jian
In this paper, we consider Kahler-Ricci flow on n-dimensional Kahler manifold with semi-ample canonical line bundle and 0< m:= Kod(X)<n. Such manifolds admit a Calabi-Yau fibration…
A remark on constant scalar curvature Kähler metrics on minimal models
Wangjian Jian, Yalong Shi, Jian Song
In this short note, we prove the existence of constant scalar curvature Kähler metrics on compact Kähler manifolds with semi-ample canonical bundles.