no. 9-10
Complex Analysis
A conformal mapping example
[Un exemple dʼapplication conforme]

Présenté par : Gilles Pisier

Smith, Wayne1 ; Volberg, Alexander2
1 Department of Mathematics, University of Hawaii, Honolulu, HI 96822, USA
2 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Comptes Rendus. Mathématique, Tome 349 (2011) no. 9-10, pp. 511-514.

On construit un exemple de deux applications conformes φ et ψ du disque unité sur le même domaine telles que le rapport φ′/ψ′ soit borné et le rapport ψ′/φ′ non borné. On donne pour cela des expressions analytiques explicites pour φ, ψ.

An example is constructed of two Riemann maps φ and ψ of the unit disk onto the same domain such that φ′/ψ′ is bounded but not bounded away from zero. This is shown by producing explicit analytic expressions of φ and ψ.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.04.010
Smith, Wayne 1 ; Volberg, Alexander 2

1 Department of Mathematics, University of Hawaii, Honolulu, HI 96822, USA
2 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA 
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Smith, Wayne; Volberg, Alexander. A conformal mapping example. Comptes Rendus. Mathématique, Tome 349 (2011) no. 9-10, pp. 511-514. doi : 10.1016/j.crma.2011.04.010. http://www.numdam.org/articles/10.1016/j.crma.2011.04.010/

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