Covering properties of meromorphic functions, negative curvature and spherical geometry

• Autores: Alexandre Eremenko, Mario Bonk
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 152, Nº 2, 2000, págs. 551-592
• Idioma: inglés
• DOI: 10.2307/2661392
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• Resumen

  • Every nonconstant meromorphic function in the plane univalently covers spherical discs of radii arbitrarily close to arctan¡î8 . 70.32¡Ç . If in addition all critical points of the function are multiple, then a similar statement holds with /2. These constants are the best possible. The proof is based on the consideration of negatively curved singular surfaces associated with meromorphic functions.