Koebe and Carathe 'odory type boundary behavior results for harmonic\n mappings

2020/05/05 by Daoud Bshouty, Jiaolong Chen, Bshouty, Daoud +5
Computer Science · Mathematics · #31A05 #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary: 30C55 #Secondary: 30C62

paper · pdf · doi:10.48550/arxiv.2005.02101

openalex publication_date 2020/05/05 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We study the behavior of the boundary function of a harmonic mapping from\nglobal and local points of view. Results related to the Koebe lemma are proved,\nas well as a generalization of a boundary behavior theorem by Bshouty, Lyzzaik\nand Weitsman. We also discuss this result from a different point of view, from\nwhich a relation between the boundary behavior of the dilatation at a boundary\npoint and the continuity of the boundary function of our mapping can be seen.\n

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