Related papers: K\"ahler stability of symplectic forms

In the first part of this paper we outline the constructions and properties of Fedosov star product and Berezin-Toeplitz star product. In the second part we outline the basic ideas and recent developments on Yau-Tian-Donaldson conjecture on…

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…

We prove the instability of conformally K\"ahler, compact or ALF Einstein 4-manifolds with nonnegative scalar curvature which are not half conformally flat. This applies to all the known examples of gravitational instantons which are not…

Let $M$ be a K\"ahler surface and $\Sigma$ be a closed symplectic surface which is smoothly immersed in $M$. Let $\alpha$ be the K\"ahler angle of $\Sigma$ in $M$. We first deduce the Euler-Lagrange equation of the functional…

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…

We prove that the existence of constant scalar curvature K\"ahler metrics with cone singularities along a divisor implies log $K$-polystability and $G$-uniform log $K$-stability, where $G$ is the automorphism group which preserves the…

In this paper, we derive a partial result related to a question of Yau: "Does a simply-connected complete K\"ahler manifold M with negative sectional curvature admit a bounded non-constant holomorphic function?" Main Theorem. Let $M^{2n}$…

Given a compact constant scalar curvature Kaehler orbifold, with nontrivial holomorphic vector fields, whose singularities admit a local ALE Kaehler Ricci-flat resolution, we find sufficient conditions on the position of the singular points…

We characterize the existence of a locally conformally K\"ahler metric on a compact complex manifold in terms of currents, adapting the celebrated result of Harvey and Lawson for K\"ahler metrics.

We obtain a compactness result for Fano manifolds and K\"ahler Ricci flows. Comparing to the more general Riemannian versions by Anderson and Hamilton, in this Fano case, the curvature assumption is much weaker and is preserved by the…

The four-dimensional effective theory for type IIB warped flux compactifications proposed in [1] is completed by taking into account the backreaction of the K\"ahler moduli on the three-form fluxes. The only required modification consists…

An almost K\"ahler structure is {\it extremal} if the Hermitian scalar curvature is a Killing potential [29]. When the almost complex structure is integrable it coincides with extremal K\"ahler metric in the sense of Calabi [8]. We observe…

We present reformulation of Mathieu's result on representing cohomology classes of symplectic manifold with symplectically harmonic forms. We apply it to the case of foliated manifolds with transversally symplectic structure and to…

Inspired by a parabolic system of Li-Yuan-Zhang and the continuity equation of La Nave-Tian, we study a system of elliptic equations for a K\"ahler metric $\omega$ and a closed $(1, 1)$-form $\alpha$. Assuming a uniform estimate for…

In this paper, we study any K\"ahler manifold where the positive orthogonal bisectional curvature is preserved on the K\"ahler Ricci flow. Naturally, we always assume that the first Chern class $C_1$ is positive. In particular, we prove…

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 introduce a notion of a K\"ahler metric with constant weighted scalar curvature on a compact K\"ahler manifold $X$, depending on a fixed real torus $\mathbb{T}$ in the reduced group of automorphisms of $X$, and two smooth (weight)…

Let $(X,\omega)$ be a compact Hermitian manifold. We establish a stability result for solutions to complex Monge-Amp\`ere equations with right-hand side in $L^p$, $p>1$. Using this we prove that the solutions are H\"older continuous with…

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…

We apply the mean curvature flow to deform symplectomorphisms of $\mathbb{CP}^n$. In particular, we prove that, for each dimension n, there exists a constant $\Lambda$, explicitly computable, such that any $\Lambda$-pinched…