The Landau theorem and Bloch theorem for planar harmonic and pluriharmonic mappings

• Autores: Huaihui Chen, Paul Gauthier
• Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 139, Nº 2, 2011, págs. 583-595
• Idioma: inglés
• DOI: 10.1090/s0002-9939-2010-10659-7
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• Resumen

  • For a normalized quasiregular pluriharmonic mapping of the unit ball of into , we estimate the supremum of numbers such that some subdomain of the ball is mapped by diffeomorphically onto some ball of radius . Our estimates significantly improve earlier estimates, even in the case of harmonic functions in the disc.