Boundary Values and Boundary Uniqueness of $J$-Holomorphic Mapping
S. Ivashkovich, J. -P. Rosay
本文对在适当意义下有界的$J$-全纯映射建立了一个Fatou型定理，并证明了其零点集的Blaschke条件.证明了$J$-全纯映射对的一个Privalov型唯一性定理。
We establish a Fatou-type Theorem for $J$-holomorphic mappings that are bounded in an appropriate sense and we prove the Blaschke condition for their zero sets. We also prove a Privalov-type uniqueness Theorem for pairs of $J$-holomorphic mappings.
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We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and restrictions on the growth of functions near the boundary of domain.
We consider inductive limits of weighted spaces of holomorphic functions in the unit ball of $\mathbb C^n$. The relationship between sets of uniqueness, weakly sufficient sets and sampling sets in these spaces is studied. In particular, the equivalence of these sets, under general conditions of the weights, is obtained.
In this paper, we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex projective space $\mathbb{P}^k$. This is a generalization of Cartan's Second Main Theorem. As a consequence, we establish a uniqueness theorem for holomorphic mappings which intersects $O(k^3)$ many totally geodesic hypersurfaces.
Uniqueness of Holomorphic Abel Functions at a Complex Fixed Point Pair
本文给出了全纯Abel函数的一个简单的唯一性判据（以及一些导出的判据），并证明了指数型的Kneser实解析Abel函数也服从这个判据。
In this article are improved and refined some of our results prior to our recent article from the journal "Russian Mathematics (Izvestiya VUZ. Matematika)" in 2015 at the expense of our latest results in 2016 on lower estimates of subharmonic functions by the logarithm module nonzero holomorphic function.
On Mok's uniqueness problem of holomorphic isometries from complex unit balls of maximal dimension into classical domains
该研究解决了Mok提出的问题，证明了从极大维复单位球到特定经典有界对称域的全纯等距嵌入均等价于Mok嵌入。
In this paper, we prove some fundamental theorems for holomorphic curves on angular domain intersecting a hypersurface, finite set of fixed hyperplanes in general position and finite set of fixed hypersurfaces in general position on complex projective variety with the level of truncation. As applications of the second main theorems for an angle, we will discuss the uniqueness problem of holomorphic curves in an angle instead of the whole complex plane. Detail, we establish a result for uniqueness problem of holomorphic curve by inverse image of a hypersurface. In my knowledge, this is the firs…
It is shown that any symplectic $2n\times 2n$-matrix, whose entries are complex holomorphic functions on a reduced Stein space, can be decomposed into a finite product of elementary symplectic matrices if and only if it is null-homotopic. Moreover, if this is the case, the number of factors can be bounded by a constant depending only on $n$ and the dimension of the space.
In this paper, we prove Huang et al.'s conjecture stated that if $f$ is a holomorphic function on $Δ^+:=\{z\in \mathbb C \colon |z|<1,~\mathrm{Im}(z)>0\}$ with $\mathcal{C}^\infty$-smooth extension up to $(-1,1)$ such that $f$ maps $(-1,1)$ into a cone $Γ_C:=\{z\in \mathbb C\colon |\mathrm{Im} (z)| \leq C|\mathrm{Re} (z)|\}$, for some positive number $C$, and $f$ vanishes to infinite order at $0$, then $f$ vanishes identically. In addition, some regularity properties of the Riemann mapping functions on the boundary and an example concerning Huang et al.'s conjecture are also given.
Approximation and accumulation results of holomorphic mappings with dense image
本文给出四个关于流形值全纯映射的逼近定理，分别用稠密像的全纯嵌入或映射逼近原映射，并构造收敛到稠密像映射的序列。
Holomorphic mappings between domains in $\mbb C^2$
在纯局部假设下证明了$\mathbb C^2$中两个区域间全纯映射的一个扩张定理。
We study proper holomorphic mappings between strictly pseudoconvex domains with low boundary regularity.
Answering all questions---concerning proper holomorphic mappings between generalized Hartogs triangles---posed by Jarnicki and Plfug (First steps in several complex variables: Reinhardt domains, 2008) we characterize the existence of proper holomorphic mappings between generalized Hartogs triangles and give their explicit form. In particular, we completely describe the group of holomorphic automorphisms of such domains and establish rigidity of proper holomorphic self-mappings on them.
In this note we establish a Schwarz type inequality for holomorphic mappings between unit balls $B_n$ and $B_m$ in corresponding complex spaces.
Stein neighborhoods of graphs of holomorphic mappings
本文给出了复流形中紧集上的全纯映射的图具有Stein邻域的充分条件。我们证明了在这些条件下，映射具有类似于$\mathbb C^n$中紧集上全纯函数的性质。
We study the boundary regularity of proper holomorphic mappings between strictly pseudoconvex domains with $C^2$-boundaries.
Regularity of Holomorphic Correspondences and Applications to the Mapping Problems
研究了全纯对应的正则性结果。作为应用，我们将它与某些新近发展的方法相结合，得到了复2-空间中具有实解析边界的区域间真全纯映射的扩张定理.
Holomorphic factorization of mappings into SL_n(C)
我们解决了Gromov的Vaserstein问题。也就是说，我们证明了从有限维约化Stein空间到SL_n（C）的零同伦全纯映射可以分解为幂单矩阵与全纯元素的有限乘积.
Recent developments in the theory of separately holomorphic mappings
我们描述了复解析空间之间的分离全纯映射理论的一部分最新发展。我们的描述集中在使用全纯光盘技术的作品。
Proper holomorphic mappings into $\ell$-concave quadric domains in projective space
本文证明了射影空间中某些$\ell$ -凹域的真全纯映射到模型二次$\ell$ -凹域的一类部分刚性结果。主要的技术结果是适当的全纯映射到模型域的程度估计，提供的映射扩展到射影空间作为有理映射，和源域包含代数簇，并具有低CR复杂度的边界。
Holomorphic mappings between pseudoellipsoids in different dimensions
我们给出了伪椭圆体实超曲面之间存在非退化全纯映射的充要条件，并为所有此类映射的集合（在它们存在的情况下）提供了显式的参数化。
A Schwarz-Pick lemma for the modulus of holomorphic mappings from the polydisk into the unit ball
本文证明了从多圆盘到单位球的全纯映射的模的一个Schwarz-Pick引理。这一结果推广了相关结果。
We prove that the space of dominant/non-constant holomorphic mappings from a product of hyperbolic Riemann surfaces of finite type into certain hyperbolic manifolds with universal cover a bounded domain is a finite set.
Holomorphic mappings into compact complex manifolds
本文的目的是给出$ \mathbb{C} $（或紧致Riemann曲面）到紧致复流形的全纯映射在次一般位置上分担因子的第二个主要定理.
Approximation and Loewner Theory of holomorphic covering mappings
本文研究了任意范数下$\u2102^n$单位球的局部一致全纯覆盖映射的逼近问题，通过发展覆盖映射的Loewner理论推广，给出了用整全纯覆盖映射逼近的条件，推动了多复变函数论中相关理论的发展。
We classify proper holomorphic mappings between generalized pseudoellipsoids of different dimensions. Those domains are parametrized by the exponents. The relations among them are also obtained. Main tool is the orthogonal decomposition of a CR bundle. Such a decomposition derives the `variable-splitting' of the mapping.
Proper holomorphic mappings between symmetrized ellipsoids
在$\mathbb{C}^n$中的一类特殊的有界$(1,2,...,n)$ -平衡域中，刻画了真全纯映射的存在性，称之为对称化椭球.利用这一结果，我们得出对称椭球类中不存在非平凡的真全纯自映射。我们还描述了这些域的自同构群。
Proper holomorphic mappings in the special class of Reinhardt domains
给出了$\C^2$中所有伪凸Reinhardt域类中域之间的真全纯映射的一个完整刻画，其对数象为一条或一个半平面.
The explicit form of proper holomorphic mappings between complex ellipsoids is given. Using this description, we characterize the existence of proper holomorphic mappings between generalized Hartogs triangles and give their explicit form. In particular, the automorphism group of such domains is found.
A Schwarz-Pick lemma for the modulus of holomorphic mappings between the unit balls in complex spaces
本文证明了复空间中单位球间全纯映射模的一个Schwarz-Pick引理。这推广了经典的Schwarz-Pick引理和Pavlovic证明的相关结果。
Note on double reflection and algebraicity of holomorphic mappings
本文的目的是在双反射条件下建立实代数CR流形之间的全纯映射的代数性，它推广了经典的单反射.还提供了各种双反射条件的完整研究。
Boundary behavior and rigidity of semigroups of holomorphic mappings
本文给出了单位圆盘上全纯自映射半群的边界渐近性态的一些定量特征，包括它们的轨道在边界Denjoy-Wolff点的极限曲率。这使我们能够建立抛物型半群的渐近刚性性质。
In this paper, we prove a general Schwarz lemma at the boundary for holomorphic mappings from the polydisc to the unit ball in any dimensions. For the special case of one complex variable, the obtained results give the classic boundary Schwarz lemma.
Projection on Segre varieties and determination of holomorphic mappings between real submanifolds
证明了将一个有限型实解析一般子流形变换成另一个实解析一般子流形的全纯映射的芽由它在目标流形的Segre簇上的投影决定.给出了一个映射到目标流形的Segre簇的芽是一个全纯映射将源流形投影到目标流形的充要条件.给出了一个应用于双全纯等价问题的例子。
On the number of factors in the unipotent factorization of holomorphic mappings into $\text{SL}_2(\mathbb{C})$
我们估计了将一个零同伦全纯映射从有限维约化Stein空间$X$分解为$\text{SL}_2(\mathbb{C})$所需的幂幺元个数.
Critical sets of proper holomorphic mappings
证明了：若一个真全纯映射$f: \mathbb C^n \to \mathbb C^N$，$1<n\le N$，将一个有限型伪凸实解析超曲面送入另一个这样的超曲面，则$f$的临界轨迹的任何$n-1$维分量与$M$的两边相交.我们将这一结果应用于$\mathbb C^n$中有界区域间真全纯映射的边界正则性问题。
In our previous work, for a given Riemann surface $Y_0$ with marked handle, we investigated geometric properties of the set of marked once-holed tori $X$ allowing holomorphic mappings of $X$ into $Y_0$. It turned out that it is a closed domain with Lipschitz boundary. In the present paper we show that the boundary is never smooth. Also, we evaluate the critical extremal length for the existence of holomorphic mappings in terms of hyperbolic lengths.
Improved Bohr-Rogosinski radius for holomorphic mappings with values in complex Banach spaces
本文把解析函数的Bohr-Rogosinski不等式推广到复Banach空间取值全纯映射，给出多圆盘与JB*-三元组情形的半径，并证明最优性。
Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold are investigated. The invariants are monotonic under holomorphic mappings and strictly monotonic under certain circumstances. Applications to holomorphic maps of annular regions in $\mathbb{C}$ and tubular neighborhoods of compact totally real submanifolds in general in $\mathbb{C}^n$, $n \geq 2$, are given. The contractibility of a hyperbolic domain with con…
A local extension theorem for proper holomorphic mappings in C^2
设f是C^2中有界域D与D'之间的真全纯映射.设M，M'分别是D和D'边界上的开片，它们是光滑的、实解析的、有限型的。设M在f下的聚值集包含在M '中。证明了f在M上全纯扩张。这可以看作是C^2中逆紧映射的Diederich-Pinchuk扩展结果的局部版本。
This expository paper is concerned with the properties of proper holomorphic mappings between domains in complex affine spaces. We discuss some of the main geometric methods of this theory, such as the Reflection Principle, the scaling method, and the Kobayashi-Royden metric. We sketch the proofs of certain principal results and discuss some recent achievements. Several open problems are also stated.
Bochner transforms, perturbations and amoebae of holomorphic almost periodic mappings in tube domains
给出了管域上全纯概周期映射的Bochner变换的闭包的另一种表示。对于这样的映射，我们引入了一个新的概念，变形虫，我们表明，映射的Ronkin的意义上是经常的，这个新的概念同意Favorov的。证明了定义在Cn上且取值于Cm+1的正则全纯概周期映射的变形虫补是Rn的Henriques m-凸子集.最后，我们比较了一些不同的正则性概念。
Applying a linearization theorem due to J. Mujica, we study the ideals of bounded holomorphic mappings $\mathcal{H}^\infty\circ\mathcal{I}$ generated by composition with an operator ideal $\mathcal{I}$. The bounded-holomorphic dual ideal of $\mathcal{I}$ is introduced and its elements are characterized as those that admit a factorization through $\mathcal{I}^\mathrm{dual}$. For complex Banach spaces $E$ and $F$, we also analyze new ideals of bounded holomorphic mappings from an open subset $U\subseteq E$ to $F$ such as $p$-integral holomorphic mappings and $p$-nuclear holomorphic mappings with…
Proper holomorphic mappings of the spectral unit ball
证明了谱单位球$Ω_n$的Alexander型定理，证明了在$Ω_n$中不存在非平凡的真全纯映射，$n\geq 2$ .
Nonvanishing of the differential of holomorphic mappings at boundary points
本文证明了C^n中具有光滑边界或实解析边界的实超曲面之间的具有不同零Jacobian的CR映射的"Hopf引理“型的一个一般结果。最后给出了这一结果在有限性和全纯可扩性方面的应用。这里的新颖之处在于，我们不假设映射或其雅可比矩阵的非平坦性，也不假设超曲面是伪凸或极小凸的。
Proper holomorphic mappings, Bells formula and the Lu Qi-Keng problem on tetrablock
考虑C^n中D到G的全纯映射，证明了它诱导Bergman空间A^2（G）与A^2（D）的某个子空间之间的酉同构.利用这个同构，我们构造了该子空间上的正交投影，并导出了Bergman核在适当的全纯映射下的Bells变换公式。由公式的推论，我们得到四嵌段结构不是陆启铿结构域。
Non-holomorphic projections and extension of biholomorphic mappings
我们证明了在一个扭曲的Bergman投影族上的正则性条件下，两个有界的伪凸光滑边界域之间的双全纯映射光滑地延伸到域的边界.这一结果受到Bell和Ligocka的启发，推广了Bell和Ligocka关于扩张的一个充分条件.
Transversality of holomorphic mappings between real hypersurfaces in different dimensions
本文考虑了不同维复空间中实超曲面之间的全纯映射。我们给出了一些条件，这意味着这样的映射是横向的目标超曲面在大多数点。
Almost periodic divisors, holomorphic functions, and holomorphic mappings
我们证明，每个几乎周期（在分布的意义上）的除数在一个管可以分配一个特殊的线丛的第一陈类玻尔的紧集所产生的除数，使平凡的上同调类表示除数的所有几乎周期的全纯函数的管。这种描述给出了几乎周期因子是全纯殆周期函数的因子的各种几何条件。给出了全纯概周期曲线的齐次坐标因子的完整描述，特别是得到了亚纯殆周期函数的因子的描述.
Proper holomorphic mappings vs. peak points and Silov boundary
本文给出了$\C$ -凸区域和对称多圆盘的某些峰函数的存在性结果。然后，我们应用后一个结果，以显示在适当的全纯映射的$A(D)$的峰值点集的等方差。此外，我们给出了一类有界伪凸Reinhardt域的峰值点集的描述。
On the complexity of proper holomorphic mappings between balls
对球间真全纯映射的研究作出了一些新的贡献。我们的结果包括有理真映射的度估计，任意真映射凸族的一个新的空隙现象，以及关于逆像的一个有趣结果。
Let $M\subset \mathbb C^n$ be a real analytic hypersurface, $M'\subset \mathbb C^N$ $(N\geq n)$ be a strongly pseudoconvex real algebraic hypersurface of the special form and $F$ be a meromorphic mapping in a neighborhood of a point $p\in M$ which is holomorphic in one side of $M$. Assuming some additional conditions for the mapping $F$ on the hypersurface $M$, we proved that $F$ has a holomorphic extension to $p$. This result may be used to show the regularity of CR mappings between real hypersurfaces of different dimensions.
Holomorphic Factorization of Mappings into $ \operatorname{Sp}_{4}( \mathbb{C}) $
本文研究映入四阶复辛群的全纯映射，证明 Stein 空间上任意零伦全纯映射均可分解为含全纯元素的初等辛矩阵有限乘积。
Non-autonomous dynamics of holomorphic mappings in projective space
研究了射影空间中全纯映射序列复合的动力学性质。我们定义遍历性和混合的非自治动力系统，我们构造完全不变测度，我们的序列满足这些属性。
Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifolds
建立了$C^\infty$类CR-映射在$C^\infty$的实解析CR-子流形和$\C^{N'}$的实代数CR-子流形之间的全纯扩张的结果.
CR transversality of holomorphic mappings between generic submanifolds in complex spaces
证明了一个将一个类属子流形映射到另一个相同维数的类属子流形的全纯映射是CR横截于目标子流形的，只要源流形是有限型，映射是类属满秩的.这个结果及其推论完全解决了Linda P. Rothschild和第一作者在2006年的一篇论文中提出的两个问题。
A unified approach to the theory of separately holomorphic mappings
本文推广了复解析空间之间的分离全纯映射理论。我们的方法是基于Poletsky理论的光盘，Rosay定理的全纯光盘和我们最近的联合工作与Pflug交叉定理在1维。它还依赖于我们的新技术的共形映射和推广的Siciak的相对极值函数。我们的方法说明了统一的特点：“从局部信息到全局扩展”。此外，它系统地避免了伯格曼型双正交基的经典方法的使用。
We prove estimates in Hölder spaces for some Cauchy-type integral operators representing holomorphic functions in Cartesian and symmetric products of planar domains. As a consequence, we obtain information on the boundary regularity in Hölder spaces of proper holomorphic maps between symmetric products of planar domains.
Holomorphic Mappings between Hyperquadrics with Small Signature Difference
本文研究了将$\bC^n$中的签名超二次曲面$\ell$发送到$\bC^N$中的签名超二次曲面$\ell'$的全纯映射.我们表明（定理\ref{main}），如果签名差$\ell'-\ell$不是太大，那么映射可以通过目标超二次曲面的自同构规范化为特别简单的形式，特别是，映射的图像包含在一个复平面中的维度仅取决于$\ell$和$\ell'$，而不是目标维度$N$。我们还证明了这类映射的一个Hopf引理型结果（定理\ref{main2}）.
Refined Bohr Inequalities and Bohr Radii Involving Schwarz Mappings for Holomorphic Functions in Banach Spaces and JB*-Triples
本文在Banach空间和JB*-三元组上建立了涉及Schwarz映射的精细Bohr不等式，推广了已有结果并获得了改进的Bohr半径。
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