相关论文: On the holomorphic convexity of nilpotent covering…

We introduce the notion of a stratified Oka manifold and prove that such a manifold $X$ is strongly dominable in the sense that for every $x\in X$, there is a holomorphic map $f:\C^n\to X$, $n=\dim X$, such that $f(0)=x$ and $f$ is a local…

In this paper, complex Hessian equation over K\"ahler manifold was studied. Under the condition that the underline K\"ahler manifold has non-negative holomorphic bisectional curvature, the existence and regularity of the solution was…

In this short note, we study compact K\"ahler surfaces whose universal cover can be realized as a quasi-projective (or quasi-K\"ahler) surface. In particular, we show that such a surface is a quotient of a torus if the universal cover is…

Theorem (uniformization). Let X be a compact Kahler manifold of dimension n with large, residually finite and nonamenable fundamental group. Then its universal covering is a bounded domain in the n-dimensional affine space.

The underlying complex structure of an ALE K\"ahler manifold is exhibited as a resolution of a deformation of an isolated quotient singularity. As a consequence, there exist only finitely many diffeomorphism types of minimal ALE K\"ahler…

Let $S$ be a smooth, totally real, compact immersion in $\mathbb{C}^n$ of real dimension $m \leq n$, which is locally polynomially convex and it has finitely many points where it self-intersects finitely many times, transversely or…

We shall show that a smooth, quasi-projective variety $X$ has a holomorphically convex universal covering $\wt X$ when (i) $\pi_1(X)$ is residually nilpotent and (ii) there is an admissable variation of \mhs\ over $X$ whose monodromy…

We prove that there exists a 1-convex surface whose universal covering does not satisfy the discrete disk property.

If $f$ is an automorphism of a compact simply connected K\"ahler manifold with trivial canonical bundle that fixes a K\"ahler class, then the order of $f$ is finite. We apply this well known result to construct compact non-K\"ahler…

This article generalises to K\"ahler orbifolds general results on uniformisation of compact K\"ahler manifolds such as the Shafarevich conjecture for linear fundamental groups.

In this paper we consider the compactness of $\beta$-symplectic critical surfaces in a K\"ahler surface. Let $M$ be a compact K\"ahler surface and $\Sigma_i\subset M$ be a sequence of closed $\beta_i$-symplectic critical surfaces with…

In this paper, we firstly generalize some theories developed by I. Ekeland and H. Hofer in [EkH] for closed characteristics on compact convex hypersurfaces in ${\bf R}^{2n}$ to star-shaped hypersurfaces. As applications, we use…

The aim of this paper is to present the first examples of compact, simply connected holomorphically pseudosymmetric Kahler manifolds.

We discuss our recent results on the existence and classification problem of complex and Kaehler structures on compact solvmanifolds. In particular, we determine in this paper all the complex surfaces which are diffeomorphic to compact…

The paper generalizes some of the well-known results for K3 surfaces to higher-dimensional irreducible symplectic (or, equivalently, compact irreducible hyperkaehler) manifolds. In particular, we discuss the projectivity of such manifolds…

Let X be a compact K\"ahler manifold such that the universal cover admits a compactification. We conjecture that the fundamental group is almost abelian and reduce it to a classical conjecture of Iitaka.

We prove that the universal covering space of a complex projective manifold is holomorphically convex provided its fundamental group is linear.

The main goal of this paper is to prove that a connected bounded geometry complete Kahler manifold which has at least 3 filtered ends admits a proper holomorphic mapping onto a Riemann surface. This also provides a different proof of the…

We present an alternative proof of the following fact: the hyperspace of compact closed subsets of constant width in $\mathbb R^n$ is a contractible Hilbert cube manifold. The proof also works for certain subspaces of compact convex sets of…

In the first part, Hyperkaehler Embeddings and Holomorphic symplectic Geometry I, we prove the following. Let $N$ be a closed analytic subvariety of a generic deformation of a holomorphically symplectic compact manifold $M$. Then the…