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Author (up) Chuaqui, M.; Hamada, H.; Hernandez, R.; Kohr, G.
Title Pluriharmonic mappings and linearly connected domains in C-n Type
Year 2014 Publication Israel Journal Of Mathematics Abbreviated Journal Isr. J. Math.
Volume 200 Issue 1 Pages 489-506
Keywords
Abstract In this paper we obtain certain sufficient conditions for the univalence of pluriharmonic mappings defined in the unit ball of C-n . The results are generalizations of conditions of Chuaqui and Hernandez that relate the univalence of planar harmonic mappings with linearly connected domains, and show how such domains can play a role in questions regarding injectivity in higher dimensions. In addition, we extend recent work of Hernandez and Martin on a shear type construction for planar harmonic mappings, by adapting the concept of stable univalence to pluriharmonic mappings of the unit ball into C-n .
Address [Chuaqui, Martin] Pontificia Univ Catolica Chile, Fac Matemat, Santiago 22, Chile, Email: mchuaqui@mat.puc.cl;
Corporate Author Thesis
Publisher Hebrew Univ Magnes Press Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0021-2172 ISBN Medium
Area Expedition Conference
Notes WOS:000338204700022 Approved
Call Number UAI @ eduardo.moreno @ Serial 389
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Author (up) 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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Author (up) Chuaqui, M.; Hernandez, R.
Title Ahlfors-Weill extensions in several complex variables Type
Year 2015 Publication Journal Fur Die Reine Und Angewandte Mathematik Abbreviated Journal J. Reine Angew. Math.
Volume 698 Issue Pages 161-179
Keywords
Abstract We derive an Ahlfors-Weill type extension for a class of holomorphic mappings defined in the ball B-n, generalizing the formula for Nehari mappings in the disk. The class of mappings holomorphic in the ball is defined in terms of the Schwarzian operator. Convexity relative to the Bergman metric plays an essential role, as well as the concept of a weakly linearly convex domain. The extension outside the ball takes values in the projective dual to C-n, that is, in the set of complex hyperplanes.
Address [Chuaqui, Martin] Pontificia Univ Catolica Chile, Fac Matemat, Santiago 22, Chile, Email: mchuaqui@mat.puc.cl;
Corporate Author Thesis
Publisher Walter De Gruyter Gmbh Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0075-4102 ISBN Medium
Area Expedition Conference
Notes WOS:000347185000006 Approved
Call Number UAI @ eduardo.moreno @ Serial 435
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Author (up) 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 (up) Chuaqui, M.; Hernandez, R.
Title Univalent harmonic mappings and linearly connected domains Type
Year 2007 Publication Journal Of Mathematical Analysis And Applications Abbreviated Journal J. Math. Anal. Appl.
Volume 332 Issue 2 Pages 1189-1194
Keywords harmonic mapping; univalent; linearly connected domain; second complex dilatation
Abstract We investigate the relationship between the univalence of f and of h in the decomposition f = h + (g) over bar of a serise-preserving harmonic mapping defined in the unit disk D subset of C. Among other results, we determine the holomorphic univalent maps It for which there exists c > 0 such that every harmonic mapping of the form f = h + (g) over bar with vertical bar g'vertical bar < c vertical bar h'vertical bar is univalent. The notion of a linearly connected domain appears in our study in a relevant way. (c) 2006 Elsevier Inc. All rights reserved.
Address Catholic Univ Chile, Santiago, Chile, Email: m.chuaqui@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:000247120600031 Approved
Call Number UAI @ eduardo.moreno @ Serial 42
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Author (up) Chuaqui, M.; Hernandez, R.; Martin, M.J.
Title Affine and linear invariant families of harmonic mappings Type
Year 2017 Publication Mathematische Annalen Abbreviated Journal Math. Ann.
Volume 367 Issue 3-4 Pages 1099-1122
Keywords
Abstract We study the order of affine and linear invariant families of planar harmonic mappings in the unit disk. By using the famous shear construction of Clunie and Sheil-Small, we construct a function to determine the order of the family of mappings with bounded Schwarzian norm. The result shows that finding the order of the class S-H of univalent harmonic mappings can be formulated as a question about Schwarzian norm and, in particular, our result shows consistency between the conjectured order of S-H and the Schwarzian norm of the harmonic Koebe function.
Address [Chuaqui, Martin] Pontificia Univ Catolica Chile, Fac Matemat, Casilla 306, Santiago, Chile, Email: mchuaqui@mat.puc.cl;
Corporate Author Thesis
Publisher Springer Heidelberg Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0025-5831 ISBN Medium
Area Expedition Conference
Notes WOS:000398175700006 Approved
Call Number UAI @ eduardo.moreno @ Serial 717
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