Two-point distortion theorems for harmonic and pluriharmonic mappings

DOI10.1090/S0002-9947-2011-05596-0zbMath1232.32007MaRDI QIDQ3103838

Hidetaka Hamada, Gabriela Kohr, Peter Duren

Publication date: 12 December 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

univalenceharmonic mappingpluriharmonic mappingaffine invariancestarlike mappingtwo-point distortionconvex mappingclose-to-convex mappinglinear invariance

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02)

Related Items (15)

Schwarz-Pick type estimates of pluriharmonic mappings in the unit polydisk ⋮ On (Fejér-)Riesz type inequalities, Hardy-Littlewood type theorems and smooth moduli ⋮ Characterizations of composition operators on Bloch and Hardy type spaces ⋮ Bohr radius for pluriharmonic mappings in separable complex Hilbert spaces ⋮ Harmonic Lipschitz type spaces and composition operators meet majorants ⋮ Distortion and covering theorems of pluriharmonic mappings ⋮ Some sharp Schwarz-Pick type estimates and their applications of harmonic and pluriharmonic functions ⋮ Schwarzian derivatives for pluriharmonic mappings ⋮ Two-point distortion theorems for harmonic mappings ⋮ Growth and distortion theorems for linearly invariant families on homogeneous unit balls in \(\mathbb C^n\) ⋮ Pluriharmonic mappings in \(\mathbb{C}^n\) and complex Banach spaces ⋮ Pluriharmonic mappings and linearly connected domains in \(\mathbb C^n\) ⋮ Distortion theorems for convex mappings on homogeneous balls ⋮ Schwarz-Pick type estimates for gradients of pluriharmonic mappings of the unit ball ⋮ Stable geometric properties of pluriharmonic and biholomorphic mappings, and Landau-Bloch's theorem

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