A Schwarz lemma for harmonic and hyperbolic-harmonic functions in higher dimensions

DOI10.1007/BF02567058zbMath0777.31003WikidataQ124819232 ScholiaQ124819232MaRDI QIDQ1210039

Bernhard Burgeth

Publication date: 16 May 1993

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155783

zbMATH Keywords

Schwarz lemmaupper and lower boundsLaplace-Beltrami operators

Mathematics Subject Classification ID

Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (30C80) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05)

Related Items (22)

A Khavinson type conjecture for hyperbolic harmonic functions on the unit ball ⋮ Schwarz-Pick lemma for harmonic and hyperbolic harmonic functions ⋮ Estimates for Convex Integral Means of Harmonic Functions ⋮ A note on the Schwarz lemma for harmonic functions ⋮ On harmonic quasiconformal quasi-isometries ⋮ Khavinson problem for hyperbolic harmonic mappings in Hardy space ⋮ Schwarz lemma for real harmonic functions onto surfaces with non-negative Gaussian curvature ⋮ Optimal estimates for hyperbolic Poisson integrals of functions in \(L^p\) with \(p > 1\) and radial eigenfunctions of the hyperbolic Laplacian ⋮ Schwarz Pick type inequalities for harmonic maps between Riemann surfaces ⋮ Distortion of quasiregular mappings and equivalent norms on Lipschitz-type spaces ⋮ On harmonic functions on surfaces with positive Gauss curvature and the Schwarz lemma ⋮ Schwarz lemma and Kobayashi metrics for harmonic and holomorphic functions ⋮ Schwarz lemma, and distortion for harmonic functions via length and area ⋮ Sharp pointwise estimates for directional derivatives of harmonic functions in a multidimensional ball ⋮ Some properties of mappings admitting general Poisson representations ⋮ A proof of the Khavinson conjecture in \(\mathbb{R}^3\) ⋮ On some Schwarz type inequalities ⋮ On pluriharmonic \(\nu\)-Bloch-type mappings and hyperbolic-harmonic mappings ⋮ Schwarz lemma for solutions of the \(\alpha\)-harmonic equation ⋮ Schwarz lemmas for mappings satisfying Poisson's equation ⋮ The boundary Schwarz lemma for harmonic and pluriharmonic mappings and some generalizations ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Best constants in the Harnack inequality for the Weinstein equation
• On the representability of harmonic functions as Newtonian potentials
• On an Extremal Problem Involving Harmonic Functions

This page was built for publication: A Schwarz lemma for harmonic and hyperbolic-harmonic functions in higher dimensions