Related papers: Unification of the K\"ahler-Ricci and Anomaly flow…

While the Anomaly flow was originally motivated by string theory, its zero slope case is potentially of considerable interest in non-Kahler geometry, as it is a flow of conformally balanced metrics whose stationary points are precisely…

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…

We generalize the maximal time existence of K\"{a}hler-Ricci flow in Tian-Zhang and Song-Tian to conical case. Furthermore, if the twisted canonical bundle $K_{M}+(1-\beta)[D]$ is big or big and nef, we can expect more on the limit…

We study the K\"ahler-Ricci flow on compact K\"ahler manifolds whose canonical bundle is big. We show that the normalized K\"ahler-Ricci flow has long time existence in the viscosity sense, is continuous in a Zariski open set, and converges…

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 consider the K\"ahler-Ricci flow on compact K\"ahler manifolds with semiample canonical bundle and intermediate Kodaira dimension, and show that the flow collapses to a canonical metric on the base of the Iitaka fibration in the locally…

Starting with a model conical K\"ahler metric, we prove a uniform scalar curvature bound for solutions to the conical K\"ahler-Ricci flow assuming a semi-ampleness type condition on the twisted canonical bundle. In the proof, we also…

In this note, we provide some general discussion on the Ricci lower bound along K\"ahler-Ricci flow with singularity over closed manifold.

In this note we propose to show that the K\"ahler-Ricci flow fits naturally within the context of the Minimal Model Program for projective varieties. In particular we show that the flow detects, in finite time, the contraction theorem of…

We show that the scalar curvature is uniformly bounded for the normalized Kahler-Ricci flow on a Kahler manifold with semi-ample canonical bundle. In particular, the normalized Kahler-Ricci flow has long time existence if and only if the…

We show that the normalized K\"ahler-Ricci flow on a compact K\"ahler manifold with semiample canonical bundle converges in the Gromov-Hausdorff topology to the metric completion of the twisted K\"ahler-Einstein metric on the canonical…

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…

The Anomaly flow is a flow which implements the Green-Schwarz anomaly cancellation mechanism originating from superstring theory, while preserving the conformally balanced condition of Hermitian metrics. There are several versions of the…

The Anomaly flow is shown to converge on toric fibrations with the Fu-Yau ansatz, for both positive and negative values of the slope parameter $\alpha'$. This implies both results of Fu and Yau on the existence of solutions for…

We study the K\"ahler-Ricci flow on a class of projective bundles $\mathbb{P}(\mathcal{O}_\Sigma \oplus L)$ over compact K\"ahler-Einstein manifold $\Sigma^n$. Assuming the initial K\"ahler metric $\omega_0$ admits a U(1)-invariant momentum…

We study the behaviour of the normalized K\"ahler-Ricci flow on complete K\"ahler manifolds of negative holomorphic sectional curvature. We show that the flow exists for all time and converges to a K\"ahler-Einstein metric of negative…

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…

Anomaly, a generic feature of relativistic quantum field theory, is shown to be present in non-relativistic classical ideal fluid. A new result is the presence of anomalous terms in current algebra, an obvious analogue of Schwinger terms…

We study the Anomaly flow on $2$-step nilmanifolds with respect to any Hermitian connection in the Gauduchon line. In the case of flat holomorphic bundle, the general solution to the Anomaly flow is given for any initial invariant Hermitian…

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…