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

By H. Chen, Paul M. Gauthier. 2011

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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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9bc3657b12725d4aa28b9d9203dd5c1168a2d013