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Title: The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing
Author: Carroll, Tom
Ortega Cerdà, Joaquim
Keywords: Teoria geomètrica de funcions
Funcions de variables complexes
Geometric function theory
Functions of complex variables
Issue Date: 29-May-2009
Publisher: Elsevier Masson
Abstract: By modifying a domain first suggested by Ruth Goodman in 1935 and by exploiting the explicit solution by Fedorov of the Polyá-Chebotarev problem in the case of four symmetrically placed points, an improved upper bound for the univalent Bloch-Landau constant is obtained. The domain that leads to this improved bound takes the form of a disk from which some arcs are removed in such a way that the resulting simply connected domain is harmonically symmetric in each arc with respect to the origin. The existence of domains of this type is established, using techniques from conformal welding, and some general properties of harmonically symmetric arcs in this setting are established.
Note: Versió postprint del document publicat a:
It is part of: Journal de Mathématiques Pures et Appliquées, 2009, vol. 92, num. 4, p. 396-406
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ISSN: 0021-7824
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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