A sharp inequality for harmonic diffeomorphisms of the unit disk
Complex Variables
2017-06-08 v1
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.
Keywords
Cite
@article{arxiv.1706.01990,
title = {A sharp inequality for harmonic diffeomorphisms of the unit disk},
author = {David Kalaj},
journal= {arXiv preprint arXiv:1706.01990},
year = {2017}
}