2016/10/04 by Hajj, Layan El
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1610.01083
A 2p-times continuously differentiable complex valued function f = u + iv in a simply connected domain is polyharmonic (or p-harmonic) if it satisfies the polyharmonic equation ΔpF = 0 . Every polyharmonic mapping f can be written as f(z) =∑kp |z|2(p-1)Gp-k+1(z) where each Gp-k+1 is harmonic. In this paper we investigate the univalence of polyharmonic mappings on linearly connected domains and the relation between univalence of f(z) and that of Gp(z). The notions of stable univalence and logpolyharminc mappings are also considered.