论文标题
普通家庭和准映射映射
Normal families and quasiregular mappings
论文作者
论文摘要
Beardon和Minda根据局部统一的Lipschitz条件来表征正常的霍明型和杂形功能家族的表征。在这里，我们将这种观点推广到较高维度的映射家族，这些映射与给定的连续性模量相对于局部均匀连续。我们的主要应用是通过局部统一的Hölder条件的Quasiregular映射家庭的正常性。这提供了一个统一的框架，在该框架中，考虑了Quasiregular映射的家族，包括恢复Miniowitz，Vuorinen等的已知结果，并产生新的结果。特别是，可以将正常的准晶格映射，Yosida准胶状映射和Bloch准胶状映射视为通过考虑域和范围的各种度量空间而产生的一类Quasiregular映射。我们给出了这些类别的几个特征，并获得了每个类别的增长率的上限。
Beardon and Minda gave a characterization of normal families of holomorphic and meromorphic functions in terms of a locally uniform Lipschitz condition. Here, we generalize this viewpoint to families of mappings in higher dimensions that are locally uniformly continuous with respect to a given modulus of continuity. Our main application is to the normality of families of quasiregular mappings through a locally uniform Hölder condition. This provides a unified framework in which to consider families of quasiregular mappings, both recovering known results of Miniowitz, Vuorinen and others, and yielding new results. In particular, normal quasimeromorphic mappings, Yosida quasiregular mappings and Bloch quasiregular mappings can be viewed as classes of quasiregular mappings which arise through consideration of various metric spaces for the domain and range. We give several characterizations of these classes and obtain upper bounds on the rate of growth in each class.
