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https://research.matf.bg.ac.rs/handle/123456789/2011| Title: | Hyperbolic metric on the strip and the Schwarz lemma for HQR mappings | Authors: | Mateljević, Miodrag Svetlik, Marek |
Affiliations: | Real and Complex Analysis | Keywords: | Harmonic functions;Holomorphic and quasiregular maps;Hyperbolic metric on the strip;Schwarz lemma;Schwarz-Pick lemma | Issue Date: | 1-Apr-2020 | Rank: | M21 | Publisher: | Beograd : Elektrotehnički fakultet | Journal: | Applicable Analysis and Discrete Mathematics | Abstract: | We give simple proofs of various versions of the Schwarz lemma for real valued harmonic functions and for holomorphic (more generally harmonic quasiregular, shortly HQR) mappings with the strip codomain. Along the way, we get a simple proof of a new version of the Schwarz lemma for real valued harmonic functions (without the assumption that 0 is mapped to 0 by the corresponding map). Using the Schwarz-Pick lemma related to distortion for harmonic functions and the elementary properties of the hyperbolic geometry of the strip we get optimal estimates for modulus of HQR mappings. |
URI: | https://research.matf.bg.ac.rs/handle/123456789/2011 | ISSN: | 14528630 | DOI: | 10.2298/AADM200104001M |
| Appears in Collections: | Research outputs |
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