Schwarz-Pick Lemma for Harmonic and Hyperbolic Harmonic Functions
Adel Khalfallah, Bojana Purti\'c, Miodrag Mateljevi\'c
TL;DR
This paper extends Schwarz-Pick inequalities to harmonic and hyperbolic harmonic functions on the unit ball, providing new bounds and disproving a recent conjecture in the field.
Contribution
It introduces new Schwarz-Pick type inequalities for harmonic and hyperbolic harmonic functions and refutes a recent conjecture by Liu.
Findings
Established inequalities of Schwarz-Pick type for harmonic functions
Disproved Liu's recent conjecture
Provided bounds for hyperbolic harmonic functions
Abstract
We establish some inequalities of Schwarz-Pick type for harmonic and hyperbolic harmonic functions on the unit ball of and we disprove a recent conjecture of Liu [Schwarz-Pick Lemma for Harmonic Functions, International Mathematics Research Notices, 2021].
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Taxonomy
TopicsAnalytic and geometric function theory · Differential Equations and Boundary Problems · Algebraic and Geometric Analysis