The Harmonic Mapping Whose Hopf Differential Is a Constant

Liang Shen
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Liang Shen: School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Mathematics, 2020, vol. 8, issue 8, 1-8

Abstract: Suppose that h ( z ) is a harmonic mapping from the unit disk D to itself with respect to the hyperbolic metric. If the Hopf differential of h ( z ) is a constant c > 0 , the Beltrami coefficient μ ( z ) of h ( z ) is radially symmetric and takes the maximum at z = 0 . Furthermore, the mapping γ : c → μ ( 0 ) is increasing and gives a homeomorphism from ( 0 , + ∞ ) to ( 0 , 1 ) .

Keywords: harmonic mapping; Hopf differential; Beltrami coefficient (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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