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Landau's theorem for p-harmonic mappings in several variables

Sh. Chen;  S. Ponnusamy;  X. Wang — 2012

Annales Polonici Mathematici

A 2p-times continuously differentiable complex-valued function f = u + iv in a domain D ⊆ ℂ is p-harmonic if f satisfies the p-harmonic equation Δ p f = 0 , where p (≥ 1) is a positive integer and Δ represents the complex Laplacian operator. If Ω ⊂ ℂⁿ is a domain, then a function f : Ω → ℂ m is said to be p-harmonic in Ω if each component function f i (i∈ 1,...,m) of f = ( f ₁ , . . . , f m ) is p-harmonic with respect to each variable separately. In this paper, we prove Landau and Bloch’s theorem for a class of p-harmonic mappings f from...

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