Related papers: Ricci flow on Kaehler manifolds

If a normalized K\"{a}hler-Ricci flow $g(t),t\in[0,\infty),$ on a compact K\"{a}hler $n$-manifold, $n\geq 3$, of positive first Chern class satisfies $g(t)\in 2\pi c_{1}(M)$ and has $L^{n}$ curvature operator uniformly bounded, then the…

In this paper, we consider $n$-dimensional compact K$\ddot{a}$hler manifold with semi-ample canonical line bundle under the long time solution of K$\ddot{a}$hler Ricci Flow. In particular, if the Kodaira dimension is one, Ricci curvature…

Let $g(t)$, $t\in [0, +\infty)$, be a solution of the normalized K\"ahler-Ricci flow on a compact K\"ahler $n$-manifold $M$ with $c_{1}(M)>0$ and initial metric $g (0)\in 2\pi c_{1}(M)$. If there is a constant $C$ independent of $t$ such…

We consider the Kaehler-Ricci flow on complete finite-volume metrics that live on the complement of a divisor in a compact Kaehler manifold X. Assuming certain spatial asymptotics on the initial metric, we compute the singularity time in…

In this paper we study a generalization of the Kahler-Ricci flow, in which the Ricci form is twisted by a closed, non-negative (1,1)-form. We show that when a twisted Kahler-Einstein metric exists, then this twisted flow converges…

For homogeneous metrics on the spaces of the title it is shown that the Ricci flow can move a metric of stricly positive sectional curvature to one with some negative sectional curvature and one of positive definite Ricci tensor to one with…

We study the convergence of the K\"ahler-Ricci flow on a compact K\"ahler manifold $(M,J)$ with positive first Chern class $c_1(M;J)$ and vanished Futaki invariant on $\pi c_1(M;J)$. As the application we establish a criterion for the…

We produce longtime solutions to the K\"ahler-Ricci flow for complete K\"ahler metrics on $\Bbb C ^n$ without assuming the initial metric has bounded curvature, thus extending results in [3]. We prove the existence of a longtime bounded…

Let $(M^3,g_0)$ be a complete noncompact Riemannian 3-manifold with nonnegative Ricci curvature and with injectivity radius bounded away from zero. Suppose that the scalar curvature $R(x)\to 0$ as $x\to \infty$. Then the Ricci flow with…

We produce complete bounded curvature solutions to K\"ahler-Ricci flow with existence time estimates, assuming only that the initial data is a smooth \K metric uniformly equivalent to another complete bounded curvature \K metric. We obtain…

In this paper, we study the stability of the conical K\"ahler-Ricci flows on Fano manifolds. That is, if there exists a conical K\"ahler-Einstein metric with cone angle $2\pi\beta$ along the divisor, then for any $\beta'$ sufficiently close…

This paper investigates the question of stability for a class of Ricci flows which start at possibly non-smooth metric spaces. We show that if the initial metric space is Reifenberg and locally bi-Lipschitz to Euclidean space, then two…

In this paper we show that on a Fano manifold the convergence of the K\"ahler-Ricci flow to a K\"ahler-Einstein metric follows from the integrability of the $L^2$ norm of the Ricci potential for positive time.

Let $g(t)$ be a complete solution to the Ricci flow on a noncompact manifold such that $g(0)$ is Kahler. We prove that if $|Rm(g(t))|_{g(t)}\le a/t$ for some $a>0$, then $g(t)$ is Kahler for $t>0$. We prove that there is a constant $…

We consider the K\"ahler-Ricci flow $\frac{\partial}{\partial t}g_{i\bar{j}} = g_{i\bar{j}} - R_{i\bar{j}}$ on a compact K\"ahler manifold $M$ with $c_1(M) > 0$, of complex dimension $k$. We prove the $\epsilon$-regularity lemma for the…

We study the asymptotic behavior of the K\"ahler-Ricci flow on K\"ahler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact K\"ahler manifold with nonnegative bounded…

We establish the existence of K\"ahler-Ricci flow on pseudoconvex domains with general initial metric without curvature bounds. Moreover we prove that this flow is simultaneously complete, and its normalized version converge to the complete…

It is observed that for complex surfaces, the positivity of the Ricci curvature is preserved by the K\"ahler-Ricci flow, under the additional assumption that the sum of the two lowest eigenvalues of the traceless curvature operator is…

The Ricci iteration is a discrete analogue of the Ricci flow. According to Perelman, the Ricci flow converges to a Kahler-Einstein metric whenever one exists, and it has been conjectured that the Ricci iteration should behave similarly.…

We show the existence of complete negative K\"ahler-Einstein metric on Stein manifolds with negatively pinched holomorphic sectional curvature. We prove that any K\"ahler metrics on such manifolds can be deformed to the complete negative…