On the univalence criteria for elliptic polyharmonic and polyelliptic-harmonic mappings

Abstract

In this paper, we first establish Landau-Bloch-type theorems for poly $(K,K^{\prime })$-elliptic harmonic mappings, which are sharp in some given cases. Thereafter, we provide several coefficient bounds for $(K,K^{\prime })$-elliptic and $K$-quasiregular polyharmonic mappings with bounded minimum distortion. Furthermore, using these coefficient bounds, we establish Landau-Bloch-type theorems for these mappings.

17 pages