Schwarzian derivative criteria for valence of analytic and harmonic mappings

• Autores: Martin Chuaqui, Peter Duren, Brad Osgood
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 143, Nº 2, 2007, págs. 473-486
• Idioma: inglés
• DOI: 10.1017/s0305004107000394
• Texto completo no disponible (Saber más ...)
• Resumen

  • For analytic functions in the unit disk, general bounds on the Schwarzian derivative in terms of Nehari functions are shown to imply uniform local univalence and in some cases finite and bounded valence. Similar results are obtained for the Weierstrass¿Enneper lifts of planar harmonic mappings to their associated minimal surfaces. Finally, certain classes of harmonic mappings are shown to have finite Schwarzian norm.