In this paper, we first establish a Schwarz-Pick lemma for higher-order derivatives of planar harmonic mappings, and apply it to obtain univalency criteria. Then we discuss distortion theorems, Lipschitz continuity an...In this paper, we first establish a Schwarz-Pick lemma for higher-order derivatives of planar harmonic mappings, and apply it to obtain univalency criteria. Then we discuss distortion theorems, Lipschitz continuity and univalency of planar harmonic mappings defined in the unit disk with linearly connected images.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
基金Supported by National Natural Science Foundation of China(Grant Nos.11401184 and 11571216)Hu’nan Province Natural Science Foundation of China(Grant No.2015JJ3025)+3 种基金the Excellent Doctoral Dissertation of Special Foundation of Hu’nan Province(higher education 2050205)the Construct Program of the Key Discipline in Hu’nan Province(Grant No.[2011]76)Academy of Finland(Grant No.278328)the Vaisala Foundation of the Finnish Academy of Science and Letters
文摘In this paper, we first establish a Schwarz-Pick lemma for higher-order derivatives of planar harmonic mappings, and apply it to obtain univalency criteria. Then we discuss distortion theorems, Lipschitz continuity and univalency of planar harmonic mappings defined in the unit disk with linearly connected images.
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.
