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On harmonic diffeomorphisms of the unit disc onto a convex domain. (English) Zbl 1041.30006
E. Heinz [Pac. J. Math. 9, 101–105 (1959; Zbl 0086.28204)] has proved that the square of the first differential of a harmonic diffeomorphism of the unit disc onto itself satisfying the condition \(w(0)=0\) bounded from below by \(1/\pi^2\). Among other results, the author generalizes this theorem for harmonic diffeomorphisms between the unit disc and convex Jordan domains.

MSC:
30C55 General theory of univalent and multivalent functions of one complex variable
Citations:
Zbl 0086.28204
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