An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,...An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,π/2） such that Re {eiδ（1-z）2f′（z）} 〉 0, z ∈ D. For the class C（k） of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.展开更多
In this article,we first establish an asymptotically sharp Koebe type covering theorem for harmonic K-quasiconformal mappings.Then we use it to obtain an asymptotically Koebe type distortion theorem,a coefficients est...In this article,we first establish an asymptotically sharp Koebe type covering theorem for harmonic K-quasiconformal mappings.Then we use it to obtain an asymptotically Koebe type distortion theorem,a coefficients estimate,a Lipschitz characteristic and a linear measure distortion theorem of harmonic K-quasiconformal mappings.At last,we give some characterizations of the radial John disks with the help of pre-Schwarzian of harmonic mappings.展开更多
In this paper we study the deformation space of certain Kleinian groups. As a result, we give a new proof of the finite Koebe theorem on Riemann surfaces from a viewpoint of Teichmüller theory.
ⅠMore than fifty years ago, Henri Cartant ~j suggested that geometric function theory ofone complex variable should be extended to biholomorphic mappings of several complexvariables. In particular, he cited the speci...ⅠMore than fifty years ago, Henri Cartant ~j suggested that geometric function theory ofone complex variable should be extended to biholomorphic mappings of several complexvariables. In particular, he cited the special classes of starlike and convex mappings asappropriate topics for generalization. In noting some of the difficulties of generalization, hepointed out the Growth Theorem as one of the results that would not extend to thepolydisc (nor to the ball). Also, he observed that for normalized biholomorphic展开更多
文摘An analytic function f in the unit disk D ：= {z ∈ C ： ｜z｜ 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k（z） ：= z/（1-z）2, z ∈ D, if there exists δ ∈ （-π/2,π/2） such that Re {eiδ（1-z）2f′（z）} 〉 0, z ∈ D. For the class C（k） of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.
基金National Natural Science Foundation of China(Grant No.12071116)the Key Projects of Hunan Provincial Department of Education(Grant No.21A0429)+3 种基金the Discipline Special Research Projects of Hengyang Normal University(Grant No.XKZX21002)the Science and Technology Plan Project of Hunan Province(Grant No.2016TP1020)the Application-Oriented Characterized Disciplines,Double First-Class University Project of Hunan Province(Xiangjiaotong[2018]469)Mathematical Research Impact Centric Support(MATRICS)of the Department of Science and Technology(DST),India(MTR/2017/000367).
文摘In this article,we first establish an asymptotically sharp Koebe type covering theorem for harmonic K-quasiconformal mappings.Then we use it to obtain an asymptotically Koebe type distortion theorem,a coefficients estimate,a Lipschitz characteristic and a linear measure distortion theorem of harmonic K-quasiconformal mappings.At last,we give some characterizations of the radial John disks with the help of pre-Schwarzian of harmonic mappings.
文摘In this paper we study the deformation space of certain Kleinian groups. As a result, we give a new proof of the finite Koebe theorem on Riemann surfaces from a viewpoint of Teichmüller theory.
文摘ⅠMore than fifty years ago, Henri Cartant ~j suggested that geometric function theory ofone complex variable should be extended to biholomorphic mappings of several complexvariables. In particular, he cited the special classes of starlike and convex mappings asappropriate topics for generalization. In noting some of the difficulties of generalization, hepointed out the Growth Theorem as one of the results that would not extend to thepolydisc (nor to the ball). Also, he observed that for normalized biholomorphic
