Compact holomorphically pseudosymmetric Kahler manifolds

退化扭子形变上的埃尔米特-辛结构与凯勒结构

Hermitian-symplectic and Kahler structures on degenerate twistor deformations

研究紧全纯辛凯勒流形的退化扭子形变结构，通过正流与Hahn-Banach定理证明其为埃尔米特辛的，再结合Huybrechts定理的版本，最终证明该退化扭子形变也是凯勒流形。

Geometric flow on compact locally conformally Kahler manifolds

We study two kinds of transformation groups of a compact locally conformally Kahler (l.c.K.) manifold. First we study compact l.c.K. manifolds with parallel Lee form by means of the existence of a holomorphic l.c.K. flow. Next, we introduce the Lee-Cauchy-Riemann (LCR) transformations as a class of diffeomorphisms preserving the specific G-structure of l.c.K. manifolds. We show that compact l.c.K. manifolds admitting a non-compact CC^* flow of LCR transformations are rigid: it is holomorphically conformal to a Hopf manifold with parallel Lee form.

紧复流形上的 p-Kähler 结构

p-Kähler structures on compact complex manifolds

本文研究紧复流形上的 p-Kähler 结构，证明相关幂零流形猜想，推导结构光滑形变的必要条件，分析其上同调类并给出多个例子。

On the Steinness of a class of Kähler manifolds

Let $(M^n, g)$ be a complete non-compact Kähler manifold with non-negative and bounded holomorphic bisectional curvature. We prove that $M$ is holomorphically covered by a pseudoconvex domain in $\C^n$ which is homeomorphic to $\R^{2n}$, provided $(M^n, g)$ has uniform linear average quadratic curvature decay.

Hopf surfaces in locally conformally Kahler manifolds with potential

An LCK manifold with potential is a compact quotient M of a Kahler manifold X equipped with a positive plurisubharmonic function f, such that the monodromy group acts on $X$ by holomorphic homotheties and maps f to a function proportional to f. It is known that M admits an LCK potential if and only if it can be holomorphically embedded to a Hopf manifold. We prove that any non-Vaisman LCK manifold with potential contains a complex surface with normalization biholomorphic to a Hopf surface H. Moreover, H can be chosen non-diagonal, hence, also not admitting a Vaisman structure.

Morrison-Kawamata cone conjecture for hyperkahler manifolds

Let $M$ be a simple holomorphically symplectic manifold, that is, a simply connected holomorphically symplectic manifold of Kahler type with $h^{2,0}=1$. We prove that the group of holomorphic automorphisms of $M$ acts on the set of faces of its Kahler cone with finitely many orbits, whenever $b_2(M)\neq 5$. This is a version of the Morrison-Kawamata cone conjecture for hyperkahler manifolds. The proof is based on the following observation, proven with ergodic theory. Let $M$ be a complete Riemannian orbifold of dimension at least three, constant negative curvature and finite volume, and $\{S_…

Diastatic entropy and rigidity of hyperbolic manifolds

Let $f: Y \rightarrow X$ be a continuous map between a compact real analytic Kähler manifold $(Y,g)$ and a compact complex {hyperbolic manifold} $(X,g_0)$. In this paper we give a lower bound of the diastatic entropy of $(Y,g)$ in terms of the diastatic entropy of $(X,g_0)$ and the degree of $f$. When the lower bound is attained we get geometric rigidity theorems for the diastatic entropy analogous to the ones obtained by G. Besson, G. Courtois and S. Gallot [2] for the volume entropy. As a corollary, when $X=Y$, we show that the minimal diastatic entropy is achieved if and only if $g$ is holo…

具有全纯平凡典范丛的六维齐性空间

Six dimensional homogeneous spaces with holomorphically trivial canonical bundle

本研究分类了6维幺模李代数，得到具有全纯平凡典范丛的紧齐性空间，还证明了紧非凯勒平衡齐性空间中Hull-Strominger系统不变解的唯一性，并在Nakamura流形上构造了杂弦运动方程的解。

Parabolic nef currents on hyperkaehler manifolds

Let M be a compact, holomorphically symplectic Kahler manifold, and $η$ a (1,1)-current which is nef (a limit of Kahler forms). Assume that the cohomology class of $η$ is parabolic, that is, its top power vanishes. We prove that all Lelong sets of $η$ are coisotropic. When M is generic, this is used to show that all Lelong numbers of $η$ vanish. We prove that any hyperkahler manifold with Pic(M) of rank 1 has non-trivial coisotropic subvarieties, if a generator of Pic(M) is parabolic.

Stone-Weierstrass 定理在 Calderón 问题中的应用

Applications of the Stone-Weierstrass theorem in the Calderón problem

本文利用 Stone-Weierstrass 定理研究 Calderón 反问题，证明了全纯可分 Kähler 流形上线性化问题及共形横截各向异性流形上非线性问题的唯一性，并推广简化了已有结果。

Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms

We construct a simply-connected compact complex non-Kähler manifold satisfying the $\partial\bar\partial$-Lemma, and endowed with a balanced metric. To this aim, we were initially aimed at investigating the stability of the property of satisfying the $\partial\bar\partial$-Lemma under modifications of compact complex manifolds and orbifolds. This question has been recently addressed and answered in \cite{rao-yang-yang, yang-yang, stelzig-blowup, stelzig-doublecomplex} with different techniques. Here, we provide a different approach using Čech cohomology theory to study the Dolbeault cohomology…

某些紧复可平行化流形及相关空间的Picard群

Picard groups of certain compact complex parallelizable manifolds and related spaces

本文计算了秩大于等于3时复半单Lie群格商空间的Picard群，确定了秩小于3时的拓扑平凡全纯线丛群，并证明了相关丛空间上Picard群的同构与单射性质。