Bloch constants for planar harmonic mappings

DOI10.1090/S0002-9939-00-05590-8zbMath0956.30012OpenAlexW1509986911MaRDI QIDQ4505874

Huai Hui Chen, Paul M. Gauthier, Walter Hengartner

Publication date: 3 October 2000

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-00-05590-8

zbMATH Keywords

harmonic mappingsBloch constant

Mathematics Subject Classification ID

Geometric function theory (30C99) Quasiconformal mappings in the complex plane (30C62)

Related Items (67)

Schwarz-Pick and Landau type theorems for solutions to the Dirichlet-Neumann problem in the unit disk ⋮ On the univalence of poly-analytic functions ⋮ On harmonic Bloch-type mappings ⋮ Norm of the pre-Schwarzian derivative, Bloch's constant and coefficient bounds in some classes of harmonic mappings ⋮ The Landau-Bloch type theorems for \(K\)-quasiregular pluriharmonic mappings ⋮ A Schwarz lemma for harmonic functions in the real unit ball ⋮ Precise values of the Bloch constants of certain log-\(p\)-harmonic mappings ⋮ A subclass of harmonic univalent mappings with a restricted analytic part ⋮ Landau-type theorems for p-harmonic mappings or log-p-harmonic mappings ⋮ Properties of some classes of planar harmonic and planar biharmonic mappings ⋮ Generalized harmonic functions and Schwarz lemma for biharmonic mappings ⋮ Bloch and Landau type theorems for pluriharmonic mappings ⋮ Several properties of \(\alpha \)-harmonic functions in the unit disk ⋮ Landau theorem for planar harmonic mappings ⋮ Theory of certain non-univalent analytic functions ⋮ Landau-type theorems of polyharmonic mappings and log-\(p\)-harmonic mappings ⋮ Landau and Bloch constants for meromorphic functions ⋮ Univalent logharmonic mappings in the plane ⋮ Estimates on Bloch constants for certain \(\log\)-\(p\)-harmonic mappings ⋮ Estimate on the Bloch constant for certain harmonic mappings under a differential operator ⋮ Bounded harmonic mappings ⋮ Landau-Bloch type theorems for certain subclasses for polyharmonic mappings ⋮ LANDAU’S THEOREM FOR SOLUTIONS OF THE -EQUATION IN DIRICHLET-TYPE SPACES ⋮ Landau-Bloch type theorem for elliptic and quasiregular harmonic mappings ⋮ Landau's theorem for functions with logharmonic Laplacian ⋮ Landau-type theorems and bi-Lipschitz theorems for bounded biharmonic mappings ⋮ Landau's theorems for biharmonic mappings ⋮ Harmonic mappings in Bergman spaces ⋮ Landau's theorems for biharmonic mappings (II) ⋮ Landau-type theorems for certain biharmonic mappings ⋮ The Schwarz-Pick lemma for planar harmonic mappings ⋮ Some properties of a class of elliptic partial differential operators ⋮ Cluster points and asymptotic values of \(C^1\) and planar harmonic functions ⋮ On harmonic \({\nu}\)-Bloch and \({\nu}\)-Bloch-type mappings ⋮ Landau's theorem for biharmonic mappings ⋮ Landau's theorem for planar harmonic mappings ⋮ LANDAU’S THEOREM AND MARDEN CONSTANT FOR HARMONIC ν-BLOCH MAPPINGS ⋮ Estimates on Bloch constants for planar harmonic mappings ⋮ COEFFICIENT ESTIMATES, LANDAU’S THEOREM AND LIPSCHITZ-TYPE SPACES ON PLANAR HARMONIC MAPPINGS ⋮ Radii of covering disks for locally univalent harmonic mappings ⋮ Radius of close-to-convexity and fully starlikeness of harmonic mappings ⋮ Landau's theorem for polyharmonic mappings ⋮ Landau's theorem for planar harmonic mappings ⋮ Some new results on planar harmonic mappings ⋮ Pluriharmonic mappings in \(\mathbb{C}^n\) and complex Banach spaces ⋮ Estimates on Bloch constants for planar harmonic mappings ⋮ Bloch constant and Landau's theorem for planar \(p\)-harmonic mappings ⋮ Landau-type theorems for certain bounded biharmonic mappings ⋮ Landau and Bloch theorems for harmonic mappings ⋮ The Landau-Bloch type theorems for planar harmonic mappings with bounded dilation ⋮ Landau-Bloch type theorems for strongly bounded harmonic mappings ⋮ Coefficients estimate for harmonic \(v\)-Bloch mappings and harmonic \(K\)-quasiconformal mappings ⋮ Another look at the Landau theorem ⋮ Landau's theorem for certain biharmonic mappings ⋮ The Landau theorem and Bloch theorem for planar harmonic and pluriharmonic mappings ⋮ Some properties of mappings admitting general Poisson representations ⋮ The Schwarz type lemmas and the Landau type theorem of mappings satisfying Poisson's equations ⋮ Schwarz type lemmas and a Landau type theorem of functions satisfying the biharmonic equation ⋮ Schwarz-type lemma, Landau-type theorem, and Lipschitz-type space of solutions to inhomogeneous biharmonic equations ⋮ On pluriharmonic \(\nu\)-Bloch-type mappings and hyperbolic-harmonic mappings ⋮ Harmonic quasiconformal mappings on the upper half-plane ⋮ Schwarzian derivative and Landau's theorem for logharmonic mappings ⋮ Landau–Bloch type theorems for certain biharmonic mappings ⋮ Landau-type theorems for certain planar harmonic mappings or biharmonic mappings ⋮ Landau-Bloch theorems for bounded biharmonic mappings ⋮ RADII OF HARMONIC MAPPINGS IN THE PLANE ⋮ Coefficient estimates and Bloch's constant in some classes of harmonic mappings

Cites Work

• Unnamed Item
• On one-to-one harmonic mappings
• On Bloch's constant
• Lewy's theorem fails in higher dimensions.
• Bloch’s theorem for real variables

This page was built for publication: Bloch constants for planar harmonic mappings