An example is constructed of two Riemann maps φ and ψ of the unit disk onto the same domain such that is bounded but not bounded away from zero. This is shown by producing explicit analytic expressions of φ and ψ.
On construit un exemple de deux applications conformes φ et ψ du disque unité sur le même domaine telles que le rapport soit borné et le rapport non borné. On donne pour cela des expressions analytiques explicites pour φ, ψ.
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Wayne Smith 1; Alexander Volberg 2
@article{CRMATH_2011__349_9-10_511_0, author = {Wayne Smith and Alexander Volberg}, title = {A conformal mapping example}, journal = {Comptes Rendus. Math\'ematique}, pages = {511--514}, publisher = {Elsevier}, volume = {349}, number = {9-10}, year = {2011}, doi = {10.1016/j.crma.2011.04.010}, language = {en}, }
Wayne Smith; Alexander Volberg. A conformal mapping example. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 511-514. doi : 10.1016/j.crma.2011.04.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.04.010/
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