Simply Connected域上的p调和测度

Improved Bohr's inequality for mappings defined on simply connected domains

In this paper, we study the Bohr phenomenon for functions that are defined on a general simply connected domain of the complex plane. We improve known results of R. Fournier and St. Ruscheweyh for a class of analytic functions. Furthermore, we examine the case where a harmonic mapping is defined in a disk containing $\mathbb{D}$ and obtain a Bohr type inequality.

Conformal Invariants in Simply Connected Domains

We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we use is based on the boundary integral equation with the generalized Neumann kernel. Several numerical examples are presented. We validate the performance and accuracy of our method by considering several model problems with known analytic solutions.

具有简单和multiply connected wandering domains的整函数

An entire function with simply and multiply connected wandering domains

我们修改了Kisaka和Shishikura的一个构造，证明了存在一个既有单连通游荡域又有多连通游荡域的整函数。此外，这些域包含在快速逃逸点的集合中。

On compact classes of solutions of Dirichlet problem in simply connected domains

The article is devoted to questions concerning the problems of compactness of solutions of the Dirichlet problem for the Beltrami equation in some simply connected domain. In terms of prime ends, we have proved results of a detailed form for the case when the maximal dilations of these solutions satisfy certain integral constraints. In addition, in this article we have proved theorems on the local and global behavior of plane and spatial mappings with direct and inverse modulus conditions.

On the geometry of simply connected wandering domains

We study the geometry of simply connected wandering domains for entire functions and we prove that every bounded connected regular open set, whose closure has a connected complement, is a wandering domain of some entire function. In particular such domain can be realized as an escaping or an oscillating wandering domain. As a consequence we obtain that every Jordan curve is the boundary of a wandering Fatou component of some entire function.

单连通性与双曲性

Simply connectedness and hyperbolicity

该研究将单连通弱特殊而非特殊的簇推广到任意维，验证其满足Campana猜想的相关部分，并首次给出任意维下满足函数域Lang猜想的光滑单连通非迷向一般型射影簇例子。

Characterizations of convergence by a given set of angles in simply connected domains

Let $Δ$ be a simply connected domain and $f:\mathbb{D} \to Δ$, where $\mathbb{D}$ is the unit disk, be a corresponding Riemann map. Let ${z_n}\subset Δ$ be a sequence with no accumulation points inside $Δ$. In the present article, we give necessary and sufficient conditions in terms of hyperbolic geometry which certify that ${f^{-1}(z_n)}$ converges to a point of $\partial \mathbb{D}$ by a certain angle $θ$ or by a certain set of angles $[θ_1, θ_2]$.

A generalization of the Bohr inequality for bounded analytic functions on simply connected domains and its applications

Bohr's classical theorem and its generalizations are now active areas of research and have been the source of investigations in numerous function spaces. In this article, we study a generalized Bohr's inequality for the class of bounded analytic functions defined on the simply connected domain $$ Ω_γ:=\bigg\{z\in \mathbb{C}: \bigg|z+\fracγ{1-γ}\bigg|<\frac{1}{1-γ}\bigg\}, \,\ \text{for } 0\leq γ<1. $$ Part of its applications, we calculate the Bohr-type radii for some known integral operators.

simply connected域上的泛Padé逼近

Universal Padé approximants on simply connected domains

泛泰勒级数理论可以推广到Padé逼近的情形，即泛逼近不再由多项式实现，而是由有理函数实现，即某些幂级数的Padé逼近。我们提出了第一个通用的结果在这个方向上，Padé逼近对应于泰勒发展的全纯函数在单连通域。只有在位于定义域之外并具有连通补的紧集$K$上才需要泛逼近。如果集合$K$另外与定义的定义域的边界不相交，则通用函数可以在边界上是光滑的。

单连通有界域中复值调和函数调和乘积的边值与零点

Boundary values and zeros of Harmonic Product of Complex-valued Harmonic Functions in a simply connected bounded Domain

本文研究复值调和函数乘积的调和性，证明其可表示为解析与共轭解析平方之差，并据此确定边值与零点上界，同时探索相关子空间的乘子和不变子空间。

单连通的小阶整函数的游荡域

Simply Connected Wandering Domains of Small Order Entire Functions

该研究展示了如何构造具有特定阶数的整函数，使其拥有有界单连通游荡域，并提供了首个此类函数的例子。

simply connected平面域上的Hardy不等式

Hardy inequalities for simply connected planar domains

1986年A.安科纳表明，使用Koebe四分之一定理，即对于一个简单连接的平面域的常数在哈代不等式与距离的边界是大于或等于1/16。在本文中，我们考虑类域的Koebe定理有一个更强的版本。这意味着更好的估计常数出现在哈代不等式。

Kähler和Riemannian流形的单连通性 via 谱估计

Simply connectedness of Kähler and Riemannian manifolds via spectral estimates

本文通过谱估计证明了Kähler和Riemannian流形的单连通性及相关拓扑性质。

simply connected域上SLE迹的连续性

Continuity of the SLE trace in simply connected domains

我们证明了在任何单连通域$G$中的$SLE_κ$迹是连续的（除了可能在其端点附近），如果$κ<8$。我们还证明了关于调和测度的支撑的Makarov定理的一个SLE模拟。

有理单纯连通品种的紧近似

Tight approximation for rationally simply connected varieties

研究证明了从复平滑射影曲线开子集到有理单纯连通品种的全纯映射可被代数映射在紧开拓扑下近似，并推导出相关结论。