Schwarz Lemma for Real Harmonic Functions onto Surfaces with Non-Negative Gaussian Curvature
Document Type
Article
Publication Date
6-15-2023
Department
Department of Mathematical Sciences
Abstract
Assume that f is a real ρ-harmonic function of the unit diskD onto the interval (-1,1), where ρ(u,v) = R(u) is a metric defined in the infinite strip (-1,1) × R. Then we prove that {equation presented} for all z ∈ D, provided that ρ has a non-negative Gaussian curvature. This extends several results in the field and answers to a conjecture proposed by the first author in 2014. Such an inequality is not true for negatively curved metrics.
Publication Title
Proceedings of the Edinburgh Mathematical Society
Recommended Citation
Kalaj, D.,
Mateljević, M.,
&
Pinelis, I.
(2023).
Schwarz Lemma for Real Harmonic Functions onto Surfaces with Non-Negative Gaussian Curvature.
Proceedings of the Edinburgh Mathematical Society,
66(2), 516-531.
http://doi.org/10.1017/S0013091523000263
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/17419