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Univalence of a complex linear combination of two extremal parallel slit mappings
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Masakazu Shiba
Published/Copyright:
September 25, 2009
Any convex combination of the so-called extremal horizontal and vertical slit mappings of a plane domain is known to be univalent. In his study on the conformal welding of annuli F. Maitani needed to know when a complex linear combination is univalent and he gave a partial answer to this problem. In the present article we give a complete answer to his and to generalized problems.
Keywords: Extremal parallel slit mappings; complex linear combination of slit mappings; univalence criteria
Received: 2006-10-18
Published Online: 2009-9-25
Published in Print: 2007-10-1
© Oldenbourg Wissenschaftsverlag
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- Universal (pluri)subharmonic functions
- Uniform approximation on the real axes by functions harmonic in a stripe and having optimal growth
- Univalence of a complex linear combination of two extremal parallel slit mappings
- Lacunary (R, p, M)-summability
- MacLane functions with prescribed zeros and interpolation properties
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Keywords for this article
Extremal parallel slit mappings;
complex linear combination of slit mappings;
univalence criteria
Articles in the same Issue
- In memoriam Gerald Schmieder
- A general cross theorem with singularities
- Bounded pointwise approximation on open Riemann surfaces
- Generalized Fourier expansion in kernels of convolution operators on Fourier hyperfunctions
- Stein's extension operator for sets with Lipγ-boundary
- On some representation formulas involving moduli of Blaschke products
- Universal (pluri)subharmonic functions
- Uniform approximation on the real axes by functions harmonic in a stripe and having optimal growth
- Univalence of a complex linear combination of two extremal parallel slit mappings
- Lacunary (R, p, M)-summability
- MacLane functions with prescribed zeros and interpolation properties
- Reasoning and proof in the mathematics classroom
