A converse to the Schwarz lemma for planar harmonic maps
Complex Variables
2021-01-12 v2
Abstract
A sharp version of a recent inequality of Kovalev and Yang on the ratio of the and norms for certain polynomials is obtained. The inequality is applied to establish a sharp and tractable sufficient condition for the Wirtinger derivatives at the origin for harmonic self-maps of the unit disc which fix the origin.
Keywords
Cite
@article{arxiv.2011.10967,
title = {A converse to the Schwarz lemma for planar harmonic maps},
author = {Ole Fredrik Brevig and Joaquim Ortega-Cerdà and Kristian Seip},
journal= {arXiv preprint arXiv:2011.10967},
year = {2021}
}
Comments
One typo corrected. This paper has been accepted for publication in Journal of Mathematical Analysis and Applications