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arXiv · 1706.01990

A sharp inequality for harmonic diffeomorphisms of the unit disk

David Kalaj
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Abstract

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.

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David Kalaj. 2017-06-06. A sharp inequality for harmonic diffeomorphisms of the unit disk. https://arxiv.org/abs/1706.01990

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