An abstract approach to Loewner chains

DOI10.1007/s11854-013-0003-4zbMath1321.32005arXiv1002.4262OpenAlexW2119965086MaRDI QIDQ351276

Filippo Bracci, Gabriela Kohr, Leandro Arosio, Hidetaka Hamada

Publication date: 11 July 2013

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.4262

zbMATH Keywords

$L^d$-evolution family $L^d$-Herglotz vector field $L^d$-Loewner chain Loewner-Kufarev PDE

Mathematics Subject Classification ID

General theory of conformal mappings (30C35) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45) Other generalizations of function theory of one complex variable (32A30)

Related Items (38)

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 $\mathbb C^n$ ⋮ Extensions of abstract Loewner chains and spirallikeness ⋮ Abstract Basins of Attraction ⋮ Extremal problems for mappings with generalized parametric representation in ${\mathbb {C}}^{n}$ ⋮ On the parametric representation of univalent functions on the polydisc ⋮ Solving the Loewner PDE in complete hyperbolic starlike domains of $\mathbb{C}^N$ ⋮ Extremal Problems and g-Loewner Chains in $$\mathbb{C}^{n}$$ and Reflexive Complex Banach Spaces ⋮ Extensions of $L^d$-Loewner chains to higher dimensions ⋮ Fekete-Szegö problem for univalent mappings in one and higher dimensions ⋮ Solution of a Loewner chain equation in several complex variables ⋮ Extension operators and support points associated with $g$-Loewner chains on complex Banach spaces ⋮ Loewner chains and nonlinear resolvents of the Carathéodory family on the unit ball in $\mathbb{C}^n$ ⋮ Nonlinear resolvents and decreasing Loewner chains ⋮ Approximation properties of univalent mappings on the unit ball in $\mathbb{C}^n$ ⋮ New subclasses of univalent mappings in several complex variables: extension operators and applications ⋮ Univalence criterion and quasiconformal extension of holomorphic mappings ⋮ Topological Loewner theory on Riemann surfaces ⋮ Extension operators and subordination chains ⋮ Spiralshapelike mappings in several complex variables ⋮ Asymptotically spirallike mappings in reflexive complex Banach spaces ⋮ Approximation properties on spirallike domains of $\mathbb{C}^n$ ⋮ Approximation of univalent mappings by automorphisms and quasiconformal diffeomorphismsin $\mathbb{C}^n$ ⋮ Chordal Loewner chains with quasiconformal extensions ⋮ Extremal properties associated with univalent subordination chains in $\mathbb C^n$ ⋮ Quasiconformal extensions, Loewner chains, and the $\lambda $-lemma ⋮ Boundary regular fixed points in Loewner theory ⋮ Convergence results for families of univalent mappings on the unit ball in C^n ⋮ Canonical models for the forward and backward iteration of holomorphic maps ⋮ Embedding univalent functions in filtering Loewner chains in higher dimension ⋮ $g$-Loewner chains, Bloch functions and extension operators in complex Banach spaces ⋮ Loewner chains, Bloch mappings and Pfaltzgraff-Suffridge extension operators on bounded symmetric domains ⋮ Some applications of variation of Loewner chains in several complex variables ⋮ Approximation and Loewner theory of holomorphic covering mappings ⋮ Loewner theory in annulus I: Evolution families and differential equations ⋮ Subclasses of biholomorphic mappings associated withg-Loewner chains on the unit ball in ℂⁿ ⋮ Semigroups versus evolution families in the Loewner theory ⋮ Classical and Stochastic Löwner–Kufarev Equations

Cites Work

This page was built for publication: An abstract approach to Loewner chains