Loewner chains and parametric representation in several complex variables
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Publication:1399330
DOI10.1016/S0022-247X(03)00127-6zbMath1029.32004OpenAlexW1986016332MaRDI QIDQ1399330
Ian Graham, Mirela Kohr, Gabriela Kohr
Publication date: 30 July 2003
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0022-247x(03)00127-6
parametric representationLoewner chainLoewner differential equationunivalent mappingtransition mapping
Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Special families of functions of several complex variables (32A17) Normal families of holomorphic functions, mappings of several complex variables, and related topics (taut manifolds etc.) (32A19)
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Cites Work
- Close-to-starlike holomorphic functions of several variables
- Extension operators for locally univalent mappings
- Loewner chains and the Roper-Suffridge extension operator
- Starlike mappings on bounded balanced domains with \(C^1\)-plurisubharmonic defining functions
- Applications of subordination chains to starlike mappings in \(\mathbb{C}^ n\)
- Subordination chains and univalence of holomorphic mappings in C\(^n\)
- Starlike and convex maps in Banach spaces
- The growth theorem and quasiconformal extension of strongly spirallike mappings of type α
- An Extension Theorem and Subclasses of Univalent Mappings in Several Complex Variables
- ON THE PARAMETRIC REPRESENTATION OF STARLIKE MAPS OF THE UNIT BALL IN CN INTO CN
- Subordination chains and quasiconformal extension of holomorphic maps in C^n
- Über die Lösungsstruktur einer Differentialgleichung in der konformen Abbildung.
- Convexity properties of holomorphic mappings in ℂⁿ
- Loewner chains and quasiconformal extension of holomorphic mappings
- Parametric Representation of Univalent Mappings in Several Complex Variables
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