2024/12/06 by Nikhil Bharti, Bharti, Nikhil, Nguyen Van Thin +1
Mathematics · Computer Science · #Analytic and geometric function theory #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2412.04808
In this paper, we study the concepts of normal functions and φ-normal functions in the framework of planar harmonic mappings. We establish the harmonic mapping counterpart of the well-known Zalcman-Pang lemma and as a consequence, we prove that a harmonic mapping whose spherical derivative is bounded away from zero is normal. Furthermore, we introduce the concept of the extended spherical derivative for harmonic mappings and obtain several sufficient conditions for a harmonic mapping to be φ-normal.