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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
##### Keywords:
complex functions; planar harmonic mappings; diffeomorphism
Zbl 0086.28204
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