A note on Schwarz-Pick lemma for bounded complex-valued harmonic functions in the unit ball of R^n
Dai Shaoyu, Pan Yifei
TL;DR
This paper extends the Schwarz-Pick lemma to bounded complex-valued harmonic functions within the unit ball of R^n, providing a new inequality that generalizes classical results to higher dimensions.
Contribution
It introduces a Schwarz-Pick lemma for harmonic functions in R^n, broadening the scope of classical complex analysis results to higher-dimensional harmonic mappings.
Findings
Established a Schwarz-Pick type inequality for harmonic functions in R^n
Generalized classical complex analysis results to higher dimensions
Provided bounds for harmonic functions in the unit ball
Abstract
In this paper we prove a Schwarz-Pick lemma for bounded complex-valued harmonic functions in the unit ball of R^n.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Nonlinear Partial Differential Equations