On harmonic functions and the Schwarz lemma
David Kalaj, Matti Vuorinen
TL;DR
This paper investigates the Schwarz lemma within the context of harmonic functions, establishing precise versions for real harmonic functions and harmonic mappings' norms, thereby advancing understanding of harmonic function behavior.
Contribution
It introduces sharp versions of the Schwarz lemma specifically tailored for real harmonic functions and the norms of harmonic mappings, filling gaps in existing harmonic analysis literature.
Findings
Established sharp Schwarz lemmas for real harmonic functions.
Derived optimal bounds for the norms of harmonic mappings.
Enhanced theoretical understanding of harmonic function constraints.
Abstract
We study the Schwarz lemma for harmonic functions and prove sharp versions for the cases of real harmonic functions and the norm of harmonic mappings.
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