English

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}
}
R2 v1 2026-06-22T20:11:14.276Z