The aim of this article is twofold. One aim is to establish the precise forms of Landau-Bloch type theorems for certain polyharmonic mappings in the unit disk by applying a geometric method. The other is to obtain the precise values of Bloch constants for certain log- p -harmonic mappings. These results improve upon the corresponding results given in Bai et al. (Complex Anal. Oper. Theory, 13(2): 321–340, 2019).

中文翻译：

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某些 log-p-harmonic 映射的 Bloch 常数的精确值

本文的目的是双重的。一个目标是通过应用几何方法为单位圆盘中的某些多谐映射建立朗道-布洛赫型定理的精确形式。另一种方法是获得某些 log-p-谐波映射的 Bloch 常数的精确值。这些结果改进了 Bai 等人给出的相应结果。(Complex Anal. Oper. Theory, 13(2): 321–340, 2019)。