Related papers: Symplectic curvature flow revisited

We introduce two new functionals on Sasaki manifolds, inspired by the work of Perelman, which are monotonic along the Sasaki-Ricci flow. We relate their gradient flow, via diffeomorphisms preserving the foliated structure of the manifold,…

We study the Kahler-Ricci flow on Fano manifolds. We show that if the curvature is bounded along the flow and if the manifold is K-polystable and asymptotically Chow semistable, then the flow converges exponentially fast to a…

In this paper, we study the behavior of Ricci flows on compact orbifolds with finite singularities. We show that Perelman's pseudolocality theorem also holds on orbifold Ricci flow. Using this property, we obtain a weak compactness theorem…

Let $(M,\bar{g})$ be a K\"ahler surface with a constant holomorphic sectional curvature $k>0$, and $\Sigma$ an immersed symplectic surface in $M$. Suppose $\Sigma$ evolves along the mean curvature flow in $M$. In this paper, we show that…

In this paper we give an explicit bound of $\Delta_{g(t)}u(t)$ and the local curvature estimates for the Ricci-harmonic flow under the condition that the Ricci curvature is bounded along the flow. In the second part these local curvature…

In 1974, S.-S. Chern and J. Simons published a paper where they defined a new type of characteristic class - one that depends not just on the topology of a manifold but also on the geometry. The goal of this paper is to investigate what…

In this work we investigate Ricci flows of almost Kaehler structures on Lie algebroids when the fundamental geometric objects are completely determined by (semi) Riemannian metrics, or effective) regular generating Lagrange/ Finsler,…

A hypersymplectic structure on a 4-manifold is a triple $\omega_1, \omega_2, \omega_3$ of 2-forms for which every non-trivial linear combination $a^1\omega_1 + a^2 \omega_2 + a^3 \omega_3$ is a symplectic form. Donaldson has conjectured…

A conjecture of Simon Donaldson is that on a compact $4$-manifold $X^4$ one can flow from a hypersymplectic structure to a hyperk\"ahler structure while remaining in the same cohomology class. To this end the hypersymplectic flow was…

Using methods from symplectic topology, we prove existence of invariant variational measures associated to the flow $\phi_H$ of a Hamiltonian $H\in C^{\infty}(M)$ on a symplectic manifold $(M,\omega)$. These measures coincide with Mather…

In this paper we study the singularities of the mean curvature flow from a symplectic surface or from a Lagrangian surface in a K\"ahler-Einstein surface. We prove that the blow-up flow $\Sigma_s^\infty$ at a singular point $(X_0, T_0)$ of…

In this paper we introduce a new geometric flow with rotational invariance and prove that, under this kind of flow, an arbitrary smooth closed contractible hypersurface in the Euclidean space Rn+1 (n, 1) converges to Sn in the C1-topology…

We prove that any singular K\"ahler--Ricci shrinker $X$ arising as a noncollapsed limit of K\"ahler--Ricci flows admits a natural structure of a locally algebraic complex-analytic variety with log terminal singularities. We then derive…

In the last 15 years, White and Huisken-Sinestrari developed a far-reaching structure theory for the mean curvature flow of mean convex hypersurfaces. Their papers provide a package of estimates and structural results that yield a precise…

We study the Ricci flow on complete Kaehler metrics that live on the complement of a divisor in a compact complex manifold. In earlier work, we considered finite-volume metrics which, at spatial infinity, are transversely hyperbolic. In…

We investigate the K\"ahler-Ricci flow modified by a holomorphic vector field. We find equivalent analytic criteria for the convergence of the flow to a K\"ahler-Ricci soliton. In addition, we relate the asymptotic behavior of the scalar…

We obtain curvature estimates for long time solutions of the continuity method on compact K\"ahler manifolds with semi-ample canonical line bundles. In this setting, initiated in arXiv:1410.3157 and arXiv:0709.0990, we adapt arguments from…

We study the local curvature estimates of long-time solutions to the normalized K\"ahler-Ricci flow on compact K\"ahler manifolds with semi-ample canonical line bundles. Using these estimates, we prove that on such a manifold, the set of…

In this paper, we study the long-term behavior of the conical K\"ahler-Ricci flow on Fano manifold $M$. First, based on our work of locally uniform regularity for the twisted K\"ahler-Ricci flows, we obtain a long-time solution to the…

This paper appears as the confluence of hyperbolic dynamics, symplectic topology and low dimensional topology, etc. We show that composite symplectic Dehn twists have certain form of nonuniform hyperbolicity: it has positive topological…