Related papers: Second Ricci flow on noncompact Hermitian manifold…

The Ricci flow is a heat equation for metrics, which has recently been used to study the topology of closed three manifolds. In this paper we apply Ricci flow techniques to general relativity. We view a three dimensional asymptotically flat…

We study noncommutative Ricci flow in a finite dimensional representation of a noncommutative torus. It is shown that the flow exists and converges to the flat metric. We also consider the evolution of entropy and a definition of scalar…

In this paper, we establish a K\"ahlerian or projectivity criterion for a class of compact Hermitian surfaces with non-positive second Chern-Ricci curvature.

In this paper we study a version of the Hermitian curvature flow (HCF). We focus on complex homogeneous manifolds equipped with induced metrics. We prove that this finite-dimensional space of metrics is invariant under the HCF and write…

We study the short-time existence and regularity of solutions to a boundary value problem for the Ricci-DeTurck equation on a manifold with boundary. Using this, we prove the short-time existence and uniqueness of the Ricci flow prescribing…

We review the main aspects of Ricci flows as they arise in physics and mathematics. In field theory they describe the renormalization group equations of the target space metric of two dimensional sigma models to lowest order in the…

We discuss a technique to construct Ricci-flat hermitian metrics on complements of (some) anticanonical divisors of almost homogeneous manifolds and discuss when this metric is complete and K\"ahler. This construction has a strong interplay…

We study $n$-dimensional Ricci flows with non-negative Ricci curvature where the curvature is pointwise controlled by the scalar curvature and bounded by $C/t$, starting at metric cones which are Reifenberg outside the tip. We show that any…

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…

Let X be a quasiprojective manifold given by the complement of a divisor $\bD$ with normal crossings in a smooth projective manifold $\bX$. Using a natural compactification of $X$ by a manifold with corners $\tX$, we describe the full…

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…

The second author and H. Yin have developed a Ricci flow existence theory that gives a complete Ricci flow starting with a surface equipped with a conformal structure and a nonatomic Radon measure as a volume measure. This led to the…

In this paper, it is elaborated the theory the Ricci flows for manifolds enabled with nonintegrable (nonholonomic) distributions defining nonlinear connection structures. Such manifolds provide a unified geometric arena for nonholonomic…

This is the second paper in a series of works devoted to nonholonomic Ricci flows. By imposing non-integrable (nonholonomic) constraints on the Ricci flows of Riemannian metrics we can model mutual transforms of generalized Finsler-Lagrange…

We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. Several geometric applications are given. In particular, (1)…

We survey some recent developments on solutions of the K\"ahler-Ricci flow on compact K\"ahler manifolds which exist for all positive times.

For any complete noncompact K$\ddot{a}$hler manifold with nonnegative and bounded holomorphic bisectional curvature,we provide the necessary and sufficient condition for non-ancient solution to the Ricci flow in this paper.

Several geometric flows on symplectic manifolds are introduced which are potentially of interest in symplectic geometry and topology. They are motivated by the Type IIA flow and T-duality between flows in symplectic geometry and flows in…

This paper has two purposes. First it partially extends the result in the author's previous work concerning the asymptotic expansion of the Tian-Yau metrics, by considering a slightly larger class of quasi-projective manifolds. This text is…

In this paper, we establish several sufficient and necessary conditions for the convergence of a K\"ahler-Ricci flow, on a K\"ahler manifold with positive first Chern class, to a K\"ahler-Einstein metric (or a shrinking K\"ahler-Ricci…