2012/04/12 by S-H Chen, Chen, SH., Saminathan Ponnusamy +3
Mathematics · #30C45 #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory #Primary: 30C65 #Secondary: 30C20
paper · pdf · doi:10.48550/arxiv.1204.2767
openalex publication_date 2012/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A 2p-times continuously differentiable complex-valued function f=u+iv in a simply connected domain Ω⊆ℂ is p-harmonic if f satisfies the p-harmonic equation Δpf=0. In this paper, we investigate the properties of p-harmonic mappings in the unit disk |z|<1. First, we discuss the convexity, the starlikeness and the region of variability of some classes of p-harmonic mappings. Then we prove the existence of Landau constant for the class of functions of the form Df=zfz-\barzf\barz, where f is p-harmonic in |z|<1. Also, we discuss the region of variability for certain p-harmonic mappings. At the end, as a consequence of the earlier results of the authors, we present explicit upper estimates for Bloch norm for bi- and tri-harmonic mappings.