Related papers: The Kahler-Ricci flow through singularities

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…

We simplify and improve the curvature estimates in the paper: On the conditions to extend Ricci flow(II). Furthermore, we develop some volume estimates for the Ricci flow with bounded scalar curvature. These estimates can be applied to…

In this paper, we prove that on a Fano manifold $M$ which admits a K\"ahler-Ricci soliton $(\om,X)$, if the initial K\"ahler metric $\om_{\vphi_0}$ is close to $\om$ in some weak sense, then the weak K\"ahler-Ricci flow exists globally and…

We prove that the conical K\"ahler-Ricci flows introduced in \cite{CYW} exist for all time $t\in [0,+\infty)$. These immortal flows possess maximal regularity in the conical category. As an application, we show if the twisted first Chern…

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 article, we study the Ricci flow neckpinch in the context of metric measure spaces. We introduce the notion of a Ricci flow metric measure spacetime and of a weak (refined) super Ricci flow associated to convex cost functions (cost…

In this paper, we construct smooth forward Ricci flow evolutions of singular initial metrics resulting from rotationally symmetric neckpinches on S^(n+1), without performing an intervening surgery. In the restrictive context of rotational…

We show that any non-collapsed finite time singularity of the Ricci flow on a compact K\"ahler surface is of Type I. Combined with a previous result of the first author, Cifarelli, and Deruelle, it follows that any such singularity is…

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…

In this paper, we prove a pseudolocality-type theorem for $\mathcal L$-complete noncompact Ricci flow which may not have bounded sectional curvature; with the help of it we study the uniqueness of the Ricci flow on noncompact manifolds. In…

We establish a short-time existence theory for complete Ricci flows under scaling-invariant curvature bounds, starting from rotationally symmetric metrics on $\mathbb{R}^{n+1}$ that are noncollapsed at infinity, without assuming bounded…

We prove the existence of Ricci flow starting from a class of metrics with unbounded curvature, which are doubly-warped products over an interval with a spherical factor pinched off at an end. These provide a forward evolution from some…

We prove the existence of Kahler-Einstein metric on a K-stable Fano manifold using the recent compactness result on Kahler-Ricci flows. The key ingredient is an algebro-geometric description of the asymptotic behavior of Kahler-Ricci flow…

In this short note, we observe that the Bamler-Kleiner proof of uniqueness and stability for 3-dimensional Ricci flow through singularities generalizes to singular Ricci flows in higher dimensions that satisfy an analogous canonical…

In this short paper, we show that K\"ahler-Ricci flows over closed manifolds would have scalar curvature blown-up for finite time singularity. Certain control of the blowing-up is achieved with some mild assumption.

We first define Pseudo-Calabi flow, as {equation*} {{aligned}{{\partial \varphi}\over {\partial t}}&= -f(\varphi), \triangle_varphi f(\varphi) &= S(\varphi) - \ul S.{aligned}. \end{equation*} Then we prove the well-posedness of this flow…

We prove a comparison theorem for the compact surfaces with negative Euler characteristic via the Ricci flow.

This is the second of two papers studying both the geometric structure of Fano fibrations and the application to K\"ahler-Ricci flows developing a singularity in finite time. We assume that the K\"ahler-Ricci flow on a compact K\"ahler…

We introduce a flow of K\"ahler structures over Fano manifolds with formal limit at infinite time a K\"ahler-Ricci soliton. This flow correspond to a Perelman's modified backward K\"ahler-Ricci type flow that we call Soliton-K\"ahler-Ricci…

In this Note we introduce and study dynamical systems related to the Ricci operator on the space of Kahler metrics as discretizations of certain geometric flows. We pose a conjecture on their convergence towards canonical Kahler metrics and…