https://orcid.org/0000-0003-3797-942X
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Abstract
We study the behavior of the boundary function of a harmonic mapping from global and local points of view. Results related to the Koebe lemma are proved, as well as a generalization of a boundary behavior theorem by Bshouty, Lyzzaik and Weitsman. We also discuss this result from a different point of view, from which a relation between the boundary behavior of the dilatation at a boundary point and the continuity of the boundary function of our mapping can be seen.
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Acknowledgments
Authors wish to thank the anonymous referee for valuable suggestions concerning the presentation of this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
The research was partly supported by National Natural Science Foundation of China (NNSF) of China [grant numbers 11801166, 11971124, 12071121, 11822105, 11901090], Academy of Finland [grant number 308063], Foundation for Aalto University Science and Technology, Natural Science Foundation of Hunan Province [grant number 2018JJ3327], China Scholarship Council, and the construct program of the key discipline in Hunan Province.