Related papers: On the weak K\"ahler-Ricci flow

These lecture notes give an introduction to the Kahler-Ricci flow. They are based on lectures given by the authors at the conference "Analytic Aspects of Complex Algebraic Geometry", held at the Centre International de Rencontres…

In this paper, we study the long-term behavior of the conical K\"ahler-Ricci flow on Fano manifold $M$. First, based on our work of locally uniform regularity for the twisted K\"ahler-Ricci flows, we obtain a long-time solution to the…

In this work, we study the H\"older regularity of the K\"ahler- Ricci flow on compact K\"ahler manifolds with semi-ample canonical line bundle. By adapting the method in the work of Hein-Tosatti on collapsing Calabi-Yau metrics, we…

In this paper, we study the moduli spaces of noncollapsed Ricci flow solutions with bounded energy and scalar curvature. We show a weak compactness theorem for such moduli spaces and apply it to study isoperimetric constant control,…

Let $(Y,g_0)$ be a compact analytic space with a finite number of singular points, where the metric at each singular point is modelled on a K\"ahler cone with smooth canonical model. We show that the K\"ahler-Ricci flow with such initial…

We study two different natural notions of singular K\"ahler-Einstein metrics on normal complex varieties. In the setting of singular Ricci flat K\"ahler cone metrics that arise as non-collapsed limits of sequences of K\"ahler-Einstein…

Studying the (long-term) behavior of the K\"ahler-Ricci flow on mildly singular varieties, one is naturally lead to study weak solutions of degenerate parabolic complex Monge-Amp\'ere equations. The purpose of this article, the first of a…

This paper investigates the twisted Calabi functional and the associated twisted Calabi flow on compact K\"ahler manifolds. Our main contributions are threefold: first, we establish the convexity of the twisted Calabi functional at its…

In this paper, we propose a method of studying the modified Kahler-Ricci flow on projective bundles and give the explicit equation from the view point of symplectic geometry.

In this paper, we announce the following results: Let M be a Kaehler-Einstein manifold with positive scalar curvature. If the initial metric has nonnegative bisectional curvature and positive at least at one point, then the K\"ahler-Ricci…

In this note, we provide some general discussion on the two main versions in the study of Kahler-Ricci flows over closed manifolds, aiming at smooth convergence to the corresponding Kahler-Einstein metrics with assumptions on the volume…

We prove that any singular K\"ahler--Ricci shrinker $X$ arising as a noncollapsed limit of K\"ahler--Ricci flows admits a natural structure of a locally algebraic complex-analytic variety with log terminal singularities. We then derive…

We establish the existence of the K"ahler-Ricci flow on projective varieties with log canonical singularities. This generalizes some of the existence results of Song-Tian \cite{ST3} in case of projective varieties with klt singularities. We…

We study the weak error associated with the Euler scheme of non degenerate diffusion processes with non smooth bounded coefficients. Namely, we consider the cases of H{\"o}lder continuous coefficients as well as piecewise smooth drifts with…

We study the generalized K\"ahler-Ricci flow with initial data of symplectic type, and show that this condition is preserved. In the case of a Fano background with toric symmetry, we establish global existence of the normalized flow. We…

We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical K\"ahler-Ricci flow on a minimal elliptic K\"ahler surface converges in the sense of currents to a generalized conical K\"ahler-Einstein…

We provide a direct proof of time-slice weak compactness along the K\"ahler Ricci flow on Fano manifolds.

For the K\"ahler-Ricci flow on a compact K\"ahler manifold with semi-ample canonical line bundle, we prove the singularity type at infinity does not depend on the choice of the initial metric. We also provide new simple proofs for some…

In our previous paper math.DG/0010008, we develop some new techniques in attacking the convergence problems for the K\"ahler Ricci flow. The one of main ideas is to find a set of new functionals on curvature tensors such that the Ricci flow…

We study the uniqueness problem for the K\"ahler-Ricci flow with a conical initial condition. Given a complete gradient expanding K\"ahler-Ricci soliton on a non compact manifold with quadratic curvature decay, including its derivatives, we…