Schwarz lemmas for mappings with bounded Laplacian

2018/10/20 by Mateljević, Miodrag, Khalfallah, Adel
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.08823

Abstract

We establish some Schwarz type Lemmas for mappings defined on the unit disk with bounded Laplacian. Then we apply these results to obtain boundary versions of the Schwarz lemma.

Related

• The Schwarz lemma at the boundary
• The Schwarz lemma for holomorphic and minimal disks at the boundary
• A note on the Schwarz lemma for harmonic functions
• A boundary Schwarz lemma for holomorphic mappings from the polydisc to the unit ball
• Extremal functions of boundary Schwarz lemma