A Class of Analytic Functions associated with Sine Hyperbolic Functions

Topological characterization of the hyperbolic maps in the Sine family

The purpose of this paper is to establish a topological characterization of all the hyperbolic maps in the Sine family $\{λ\sin(z) \:\big{|}\:λ\ne 0\}$ which have super-attracting cycles.

复化的广义正弦函数

Generalized Sine Functions, Complexified

该研究探讨了参数化广义单位圆的广义正弦函数$\n_n$的复解析拓展，确定了其作为多边形到带n条割线复平面共形等价映射的自然定义域，并给出相关几何与解析应用。

带两个参数的广义正弦函数的实解析性

Real-Analyticity of Generalized Sine Functions with Two Parameters

该研究针对带双参数的广义正弦函数sin_{p,n}，通过分析其在特定点的解析条件与泰勒收敛半径，确定了该函数为实解析的最大实区间，拓展了广义三角函数的解析性质相关结论。

Gap probabilities for the cardinal sine

We study the zero set of random analytic functions generated by a sum of the cardinal sine functions that form an orthogonal basis for the Paley-Wiener space. As a model case, we consider real-valued Gaussian coefficients. It is shown that the asymptotic probability that there is no zero in a bounded interval decays exponentially as a function of the length.

Complex-analytic intermediate hyperbolicity, and finiteness properties

Motivated by the finiteness of the set of automorphisms Aut(X) of a projective manifold X, and by Kobayashi-Ochiai's conjecture that a projective manifold dim(X)-analytically hyperbolic (also known as strongly measure hyperbolic) should be of general type, we investigate the finiteness properties of Aut(X) for a complex manifold satisfying a (pseudo-) intermediate hyperbolicity property. We first show that a complex manifold X which is (dim(X) -- 1)-analytically hyperbolic has indeed finite automorphisms group. We then obtain a similar statement for a pseudo-(dim(X) -- 1)-analytically hyperbol…

几乎保持双曲面积的单位圆盘解析映射

Analytic mappings of the unit disk which almost preserve hyperbolic area

本文研究对大双曲圆盘面积扭曲有界的单位圆盘解析自映射，通过角导数、Lipschitz扩张、Möbius扭曲、临界点分布及Aleksandrov-Clark测度等对其进行刻画，并探讨了相关测度的Lyapunov指数。