Extreme points, support points and the Loewner variation in several complex variables

DOI10.1007/s11425-012-4376-0zbMath1257.32012OpenAlexW1982367292MaRDI QIDQ1934437

Hidetaka Hamada, Mirela Kohr, Ian Graham, Gabriela Kohr

Publication date: 28 January 2013

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-012-4376-0

zbMATH Keywords

biholomorphic mapping reachable set parametric representation Loewner chain starlike mapping

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 (22)

Bounded support points for mappings with $g$-parametric representation in $\mathbb{C}^2$ ⋮ Variation of Loewner chains, extreme and support points in the class $S^0$ in higher dimensions ⋮ 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 ${\mathbb {C}}^{n}$ ⋮ On reachable families of the Loewner differential equation in several complex variables ⋮ On support points of the class $S^0(B^n)$ ⋮ Rogosinski's lemma for univalent functions, hyperbolic Archimedean spirals and the Loewner equation ⋮ On the parametric representation of univalent functions on the polydisc ⋮ Extremal Problems and g-Loewner Chains in $$\mathbb{C}^{n}$$ and Reflexive Complex Banach Spaces ⋮ Extension operators and automorphisms ⋮ Extreme points, support points and $g$-Loewner chains associated with Roper-Suffridge and Pfaltzgraff-Suffridge extension operators ⋮ Loewner chains and nonlinear resolvents of the Carathéodory family on the unit ball in $\mathbb{C}^n$ ⋮ Extension operators and subordination chains ⋮ Support Points and the Bieberbach Conjecture in Higher Dimension ⋮ Extremal Problems for Mappings with g-Parametric Representation on the Unit Polydisc in ℂ n ⋮ Extremal properties associated with univalent subordination chains in $\mathbb C^n$ ⋮ Convergence results for families of univalent mappings on the unit ball in C^n ⋮ Growth and distortion results for a class of biholomorphic mapping and extremal problem with parametric representation in $\mathbb{C}^n$ ⋮ Some applications of variation of Loewner chains in several complex variables ⋮ Shearing process and an example of a bounded support function in $S^0(\mathbb B^2)$ ⋮ A density result for parametric representations in several complex variables

Cites Work

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