Heinz-Schwarz inequalities for harmonic mappings in the unit ball

DOI10.5186/aasfm.2016.4126zbMath1346.31002OpenAlexW4248652415MaRDI QIDQ2790833

David Kalaj

Publication date: 8 March 2016

Published in: Annales Academiae Scientiarum Fennicae Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5186/aasfm.2016.4126

zbMATH Keywords

harmonic mappingsSchwarz inequalityHeinz inequality

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05)

Related Items (16)

General Heinz-Schwarz type inequalities for certain mappings in space ⋮ Schwarz-Pick lemma for harmonic and hyperbolic harmonic functions ⋮ Generalized harmonic functions and Schwarz lemma for biharmonic mappings ⋮ Boundary Schwarz lemma for harmonic and pluriharmonic mappings in the unit ball ⋮ Schwarz-type lemma at the boundary for mappings satisfying non-homogeneous polyharmonic equations ⋮ The Heinz type inequality, Bloch type theorem and Lipschitz characteristic of polyharmonic mappings ⋮ Some inequalities for self-mappings of unit ball satisfying the invariant Laplacians ⋮ Some properties of a class of elliptic partial differential operators ⋮ Radó-Kneser-Choquet theorem for harmonic mappings between surfaces ⋮ Some properties of mappings admitting general Poisson representations ⋮ Schwarz-Pick type estimates for gradients of pluriharmonic mappings of the unit ball ⋮ 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 ⋮ Schwarz lemmas for mappings satisfying Poisson's equation ⋮ The boundary Schwarz lemma for harmonic and pluriharmonic mappings and some generalizations

Cites Work

• Schwarz lemma at the boundary of the unit ball in \(\mathbb C^n\) and its applications
• Some properties of a class of elliptic partial differential operators
• Sharp pointwise estimates for directional derivatives of harmonic functions in a multidimensional ball
• Harmonic quasiconformal self-mappings and Möbius transformations of the unit ball
• On one-to-one harmonic mappings
• An Extremal Problem for Harmonic Functions in the Ball
• On harmonic functions and the Schwarz lemma
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