arXiv research

We introduce a flow of Kähler structures over Fano manifolds with formal limit at infinite time a Kähler-Ricci soliton. This flow correspond to a Perelman's modified backward Kähler-Ricci type flow that we call Soliton-Kähler-Ricci flow. It can be generated by the Soliton-Ricci flow. We assume that the Soliton-Ricci fl…

Survey on Kähler-Ricci flow solutions.

Proof of flow convergence on Fano manifolds.

Kähler-Ricci flow on Kähler manifolds converges to negative Kodaira dimension

Enhances understanding of Kähler-Ricci flow singularities.

In this paper, we study the long-term behavior of the conical Kähler-Ricci flow on Fano manifold $M$. First, based on our work of locally uniform regularity for the twisted Kähler-Ricci flows, we obtain a long-time solution to the conical Kähler-Ricci flow by limiting a sequence of these twisted flows. Second, we study…

We introduce the conical Kähler-Ricci flow modified by a holomorphic vector field. We construct a long-time solution of the modified conical Kähler-Ricci flow as the limit of a sequence of smooth Kähler-Ricci flows.

Study K-R flow on Hirzebruch surfaces, showing tangent flows are K-R flows with orbifold singularities.

Clarifies definition of polarized canonical radius in Kahler Ricci flow.

Ancient solutions to Kähler Ricci flow classified completely.

Kahler-Ricci flow long-time behavior and initial data

In this paper, we prove the existence of a Kahler Ricci soliton on any smooth Fano horospherical manifold by a study of the Kahler-Ricci flow. Indeed, we prove that the renormalized Kahler Ricci flow converges in the sense of Cheeger Gromov and that this limit is a Kahler-Ricci soliton.

Kähler-Ricci flow shows type II singularity on Fano threefolds.

The paper analyzes Kähler-Ricci flow near Kähler-Ricci solitons under complex structure deformation.

Study shows flow convergence to smooth K-Ricci outside a divisor with cusp singularity.

Paper studies Kähler-Ricci flow convergence on Fano manifolds.

We prove the convergence of Kähler-Ricci flow with some small initial curvature conditions. As applications, we discuss the convergence of Kähler-Ricci flow when the complex structure varies on a Kähler-Einstein manifold.

In this short note we announce a regularity theorem for Kähler-Ricci flow on a compact Fano manifold (Kähler manifold with positive first Chern class) and its application to the limiting behavior of Kähler-Ricci flow on Fano 3-manifolds. Moreover, we also present a partial $C^0$ estimate to the Kähler-Ricci flow under …

This paper proves uniqueness of Kähler-Ricci flow on non-compact manifolds.

Paper shows regularizing flow for conical Kähler-Ricci equations.

We investigate the limiting behavior of the unnormalized Kahler-Ricci flow on a Kahler manifold with a polarized initial Kahler metric. We prove that the Kahler-Ricci flow becomes extinct in finite time if and only if the manifold has positive first Chern class and the initial Kahler class is proportional to the first …

The Kähler-Ricci flow's singularities are analyzed with bounds and convergence results.

Kähler-Ricci flow smooths out positive closed currents with divisorial singularities

In this paper, we prove that Kähler-Ricci flow converges to a Kähler-Einstein metric (or a Kähler-Ricci soliton) in the sense of Cheeger-Gromov as long as an initial Kähler metric is very closed to $g_{KE}$ (or $g_{KS}$) if a compact Kähler manifold with $c_1(M)>0$ admits a Kähler Einstein metric $g_{KE}$ (or a Kähler-…

The Kähler-Ricci flow near conical singularities is described with a $C/t$ curvature bound.

Weak base-point freeness leads to Kähler-Ricci flow diameter bounds.

Proves estimates for Kähler-Ricci flow solutions.

In this note, a modified Kähler-Ricci flow is introduced and studied. The main point is to show the flexibility of Kähler-Ricci flow and summarize some useful techniques.

In this note, we prove that on an $n$-dimensional compact toric manifold with positive first Chern class, the Kähler-Ricci flow with any initial $(S^1)^n$-invariant Kähler metric converges to a Kähler-Ricci soliton. In particular, we give another proof for the existence of Kähler-Ricci solitons on a compact toric manif…

The Kähler-Ricci flow smooths positive currents on Kähler manifolds.

In this paper, by limiting twisted conical Kähler-Ricci flows, we prove the long-time existence and uniqueness of cusp Kähler-Ricci flow on compact Kähler manifold $M$ which carries a smooth hypersurface $D$ such that the twisted canonical bundle $K_M+D$ is ample. Furthermore, we prove that this flow converge to a uniq…

Paper studies limits of Kähler-Ricci flow on Fano G-manifolds.

We investigate Riemannian (non-Kahler) Ricci flow solutions that develop finite-time Type-I singularities and present evidence in favor of a conjecture that parabolic rescalings at the singularities converge to singularity models that are shrinking Kahler-Ricci solitons. Specifically, the singularity model for these so…

Study Ricci flow on CP1-bundles over Kähler-Einstein manifolds.

Quantizes Kähler-Ricci flow for Fano manifolds.

The paper connects complex normalizing flows to Kähler-Ricci flows using geometric and statistical perspectives.

Flow analysis leads to metric completion in Kähler geometry.

Kähler-Ricci flow on spherical Fano manifolds converges to a soliton.

Study on Kähler-Ricci flow's Hölder regularity on compact manifolds.

The paper studies Ricci curvature on Kähler-Ricci flow.

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 exponentially. This generalizes a result of Perelman on the convergence of the Kahler-Ric…

The paper studies how certain currents can induce metric structures from Kähler-Ricci flows.

The Kähler-Ricci flow yields bounded diameter and Ricci curvature for minimal models.

Uniform Laplace comparison for Kähler Ricci flow on Fano manifolds.

The paper studies a degenerate equation related to Kähler-Ricci flow on symplectic quotients.

We prove the existence and uniqueness of the weak Kahler-Ricci flow on projective varieties with log terminal singularities. It is also shown that the weak Kahler-Ricci flow can be uniquely continued through divisorial contractions and flips if they exist. We then propose an analytic version of the Minimal Model Progra…

Study Kähler-Ricci flow on manifolds with singularities.

We investigate the Chern-Ricci flow, an evolution equation of Hermitian metrics generalizing the Kahler-Ricci flow, on elliptic bundles over a Riemann surface of genus greater than one. We show that, starting at any Gauduchon metric, the flow collapses the elliptic fibers and the metrics converge to the pullback of a K…