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On the existence of the Green function for the most general simply connected plane region. (On the existence of the Green’s function for the most general simply connected plane region.) (English) JFM 31.0420.01
Das Problem, das Innere eines einfach zusammenhängenden ebenen Gebietes T conform auf das Innere eines Kreises abzubilden, erfordert bekanntlich den Nachweis der Existenz der dem Gebiete T entsprechenden Green’schen Function. Die bisherigen Beweise (Schwarz, Paraf, Painlevé u. s. w.) setzen eine besondere Beschaffenheit der Grenzcurve voraus. Unter Verwendung einer Methode, die im Grunde mit einer von Poincaré benutzten [S. M. F. Bull. 11] übereinstimmt, liefert Verf. in vorliegender Arbeit den erforderlichen Existenznachweis der Green’schen Function für das allgemeinste einfach zusammenhängende ebene Gebiet.

30C35General theory of conformal mappings