Variation of Loewner chains, extreme and support points in the class \(S^0\) in higher dimensions

DOI10.1007/s00365-015-9302-6zbMath1341.32012arXiv1402.5538OpenAlexW1685991110MaRDI QIDQ272902

Gabriela Kohr, Filippo Bracci, Hidetaka Hamada, Ian Graham

Publication date: 21 April 2016

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.5538

zbMATH Keywords

holomorphic mappings of several variablesLoewner chainsvariation of Loewner chains

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02)

Related Items (27)

Bounded support points for mappings with \(g\)-parametric representation in \(\mathbb{C}^2\) ⋮ Support points and extreme points for mappings with \(A\)-parametric representation in \(\mathbb C^n\) ⋮ Support points for families of univalent mappings on bounded symmetric domains ⋮ Extremal problems for mappings with generalized parametric representation in \({\mathbb {C}}^{n}\) ⋮ The Fekete and Szegö inequality for a class of holomorphic mappings on the unit polydisk in and its application ⋮ On reachable families of the Loewner differential equation in several complex variables ⋮ On refinement of the coefficient inequalities for a subclass of quasi-convex mappings in several complex variables ⋮ On the parametric representation of univalent functions on the polydisc ⋮ Fekete-Szegö problem for univalent mappings in one and higher dimensions ⋮ The Fekete-Szegö inequality and successive coefficients difference for a subclass of close-to-starlike mappings in complex Banach spaces ⋮ Loewner chains and nonlinear resolvents of the Carathéodory family on the unit ball in \(\mathbb{C}^n\) ⋮ An embedding of the unit ball that does not embed into a Loewner chain ⋮ New subclasses of univalent mappings in several complex variables: extension operators and applications ⋮ Support Points and the Bieberbach Conjecture in Higher Dimension ⋮ Extremal Problems for Mappings with g-Parametric Representation on the Unit Polydisc in ℂ n ⋮ Spiralshapelike mappings in several complex variables ⋮ On the coefficient inequalities for a class of holomorphic mappings associated with spirallike mappings in several complex variables ⋮ Approximation of univalent mappings by automorphisms and quasiconformal diffeomorphismsin \(\mathbb{C}^n\) ⋮ Some refinements of the Fekete and Szegő inequality on bounded starlike circular domains in \(\mathbb{C}^n\) ⋮ On the coefficient inequality on a bounded starlike circular domain in \(\mathbb{C}^n\) ⋮ Convergence results for families of univalent mappings on the unit ball in C^n ⋮ A refinement of the coefficient inequalities for a subclass of starlike mappings in several complex variables ⋮ The Fekete-Szegö problem for starlike mappings and nonlinear resolvents of the Carathéodory family on the unit balls of complex Banach spaces ⋮ Some refinements of the Fekete and Szegö inequalities in one and higher dimensions ⋮ Shearing process and an example of a bounded support function in \(S^0(\mathbb B^2)\) ⋮ Fekete and Szegö inequality for a subclass of almost spirallike mappings of type β and order α on the bounded starlike circular domain in ℂ ⁿ ⋮ A density result for parametric representations in several complex variables

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