A Sharp Inequality for Harmonic Diffeomorphisms of the Unit Disk



We extend the classical Schwarz–Pick inequality to the class of harmonic mappings between the unit disk and a Jordan domain with given perimeter. It is intriguing that the extremals in this case are certain harmonic diffeomorphisms between the unit disk and a convex domain that solve the Beltrami equation of second order.


Harmonic functions Convex domain Hardy spaces 

Mathematics Subject Classification

Primary 31R05 Secondary 42B30 



I am grateful to the referee for useful suggestions and corrections.


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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.Faculty of Natural Sciences and MathematicsUniversity of MontenegroPodgoricaMontenegro

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