凸域内单叶函数的导数

设函数f（w）为凸区域D内的单叶解析函数,对于2≤n≤8和所有w∈D,本文得到估计式|f（n）（w）/f＇（w）|的精确上界.这个结果推广了一些已知的结论.     

Sub-Riemannian geometry of the coefficients of univalent functions

We consider coefficient bodies Mn for univalent functions. Based on the Löwner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov's operators for a representation of the Virasoro algebra. Then Mn are defined as sub-Riemannian manifolds. Given a Lie-Poisson bracket they form a grading of subspaces with the first subspace as a bracket-generating distribution of complex dimension two. With this sub-Riemannian structure we construct a new Hamiltonian system to calculate regular geodesics which turn to be horizontal. Lagrangian formulation is also given in the particular case M₃.     

Mapping properties of nonlinear integral operators and pre-Schwarzian derivatives

In this paper, nonlinear integral operators on normalized analytic functions in the unit disk are investigated in connection with the pre-Schwarzian derivative and the Hornich operation. In particular, several nontrivial relations between these operators and the class of strongly starlike functions will be deduced.     

On harmonic typically real mappings

In this paper, we prove that a univalent orientation-preserving harmonic mapping defined on the unit disk U with the normalization f(0)=0, , is a typically real mapping, if f(U) is a starlike domain with respect to the origin or f(U) is convex in one direction.     

On support points of univalent functions and a disproof of a conjecture of Bombieri

We consider the linear functional for on the set of normalized univalent functions in the unit disk and use the result to disprove a conjecture of Bombieri.

     

Landau's theorem for biharmonic mappings

In this paper, we show the existence of Landau constant for biharmonic mappings of the form F(z)=²|z|G(z)+K(z), |z|<1, where G and K are harmonic.     

A Generalization of Univaleby Functions with Negative Coefficients

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Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation

Let B be the unit ball in Cn with respect to an arbitrary norm and let f(z,t) be a g-Loewner chain such that e−tf(z,t)−z has a zero of order k+1 at z=0. In this paper, we obtain growth and covering theorems for . Moreover, we consider coefficient bounds and examples of mappings in .     

一类解析函数类的Hankel行列式的上界估计

本文对在单位圆盘U={z∈C：l│z│〈1}内解析且满足（1-λ）f（z）/z＋λf^1（z）〈1＋Az/1＋Bz（-1≤B＜A≤1;z∈U的函数f所对应的Hankel行列式│a2a4-a^23│,利用Toeplitz行列式的性质得到了其上界估计。