Геометрија, образовање и визуализација са применама, 7. март 2019.

• 06. Март, 2019
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Наредни састанак Семинара биће одржан у четвртак, 7. марта 2019. у сали 301ф Математичког института САНУ са почетком у 17:15.

Предавач: Миодраг Матељевић, Математички факултет-Универзитет у Београду, САНУ

Наслов предавања: HYPERBOLIC METRIC ON THE STRIP AND THE SCHWARZ LEMMA FOR HQR MAPPINGS

Апстракт: In this talk 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 using the principle of subordination and the corresponding conformal mapping 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 mappings and the elementary properties of the hyperbolic geometry of the strip we get optimal estimates for modulus of HQR mappings. This is joint work with Marek Svetlik.

References:
[1] M. Mateljević, M. Svetlik, Hyperbolic metric on the strip and the Schwarz lemma for HQR mappings, arXiv:1808.06647v1 [math.CV], http://arxiv.org/abs/1808.06647
[2] M. Mateljević, Schwarz lemma and Kobayashi metrics for harmonic and holomorphic functions. J. Math. Anal. Appl. 464 (2018) 78-100.