A Schwarz lemma for two families of domains and complex geometry. Issue 5 (4th May 2021)

• Record Type: Journal Article
• Authors: Pal, Sourav; Roy, Samriddho
• Is Part Of: Complex variables and elliptic equations. Volume 66:Issue 5(2021)
• Page Start: 756
• Page End: 782
• Publication Date: 2021-05-04
• Subjects: H. Boas; Symmetrized polydisc -- extended symmetrized polydisc -- complex geometry -- Schwarz lemma -- interpolating function; 30C80 -- 32A10 -- 32A60 -- 32E20 -- 32E30; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1743983
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : We make sharp estimates to obtain a Schwarz-type lemma for the symmetrized polydisc G n and for the extended symmetrized polydisc G ~ n . We explicitly construct an interpolating function under certain condition. To do so, we followed the methods described in [Young NJ. The automorphism group of the tetrablock. J Lond Math Soc. 2008;77(2):757–770]. Also we find a few geometric interplay between the members of the family G ~ n and its closure Γ ~ n .