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.

中文翻译：

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谐波映射的 Koebe 和 Caratheódory 类型边界行为结果

我们从全局和局部的角度研究谐波映射的边界函数的行为。证明了与 Koebe 引理相关的结果，以及 Bshouty、Lyzzaik 和 Weitsman 对边界行为定理的推广。我们还从不同的角度讨论了这个结果，从中可以看出边界点处扩张的边界行为与我们映射的边界函数的连续性之间的关系。