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Author Chuaqui, M.; Hernandez, R.
Title The order of a linearly invariant family in C-n Type
Year 2013 Publication Journal Of Mathematical Analysis And Applications Abbreviated Journal J. Math. Anal. Appl.
Volume 398 Issue 1 Pages 372-379
Keywords Linearly invariant family; Bergman metric; Schwarzian operator; Trace order; Variational method; Extremal mapping
Abstract We study the (trace) order of the linearly invariant family in the ball B-n defined by parallel to SF parallel to <= alpha, where F : B-n -> C-n is locally biholomorphic and SF is the Schwarzian operator. By adapting Pommerenke's approach, we establish a characteristic equation for the extremal mapping that yields an upper bound for the order of the family in terms of alpha and the dimension n. Lower bounds for the order are established in similar terms by means of examples. (C) 2012 Elsevier Inc. All rights reserved.
Address [Chuaqui, Martin] Pontificia Univ Catolica Chile, Fac Matemat, Santiago 22, Chile, Email: mchuaqui@mat.puc.cl;
Corporate Author Thesis
Publisher Academic Press Inc Elsevier Science Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0022-247x ISBN Medium
Area Expedition Conference
Notes WOS:000310659500031 Approved
Call Number UAI @ eduardo.moreno @ Serial 252
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Author Chuaqui, M.; Hernandez, R.
Title Families of homomorphic mappings in the polydisk Type
Year 2023 Publication Complex Variables And Elliptic Equations Abbreviated Journal Complex Var. Elliptic. Equ.
Volume Early Access Issue Pages
Keywords Schwarzian operator; polydiskl; ocally biholomorphic; norm; covering
Abstract We study classes of locally biholomorphic mappings defined in the polydisk P-n that have bounded Schwarzian operator in the Bergman metric. We establish important properties of specific solutions of the associated system of differential equations, and show a geometric connection between the order of the classes and a covering property. We show for modified and slightly larger classes that the order is Lipschitz continuous with respect to the bound on the Schwarzian, and use this to estimate the order of the original classes.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1747-6933 ISBN Medium
Area Expedition Conference
Notes WOS:001026714000001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1841
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