论文标题
准图映射的最大模量集
The maximum modulus set of a quasiregular map
论文作者
论文摘要
我们首次研究了准毛图的最大模量集。很容易看出这些集合必须关闭，并且至少包含每个模量的一个点。 Blumenthal表明，对于整个地图，这些集合是整个平面，或者是可数的分析曲线结合。我们表明，在准牙齿的情况下，通过对比的方式，可以将任何模量至少一个点的封闭集作为Quasiregular MAP的最大模量集。这些例子都是多项式类型。我们还表明，只要受到附加的约束，甚至可以通过超验类型的准图表来实现此类集合。
We study, for the first time, the maximum modulus set of a quasiregular map. It is easy to see that these sets are necessarily closed, and contain at least one point of each modulus. Blumenthal showed that for entire maps these sets are either the whole plane, or a countable union of analytic curves. We show that in the quasiregular case, by way of contrast, any closed set containing at least one point of each modulus can be attained as the maximum modulus set of a quasiregular map. These examples are all of polynomial type. We also show that, subject to an additional constraint, such sets can even be attained by quasiregular maps of transcendental type.
