论文标题
玫瑰花塞谐波映射
Rosette Harmonic Mappings
论文作者
论文摘要
谐波映射是一个复杂变量的单价谐波函数。我们在设备磁盘上定义了一个谐波映射的家族，其图像是旋转的对称玫瑰花结，带有$ n $ cusps或n个节点，其中$ n \ ge 3 $。这些映射类似于$ n $ cused的低温小组，但在分析和共分析部件中都通过高斯高几何因素进行了修改。分析和抗分析部件的角度$β$相对旋转导致具有循环的图形，在某些情况下，二$ n $的二面对称性。虽然不同$β$的图可能是不同的，但尖端沿着独立于$β$的轴对齐。对于$β$的某些孤立值，边界函数与恒定弧连续，并且具有内部角度$π/2-π/n $的节点。
A harmonic mapping is a univalent harmonic function of one complex variable. We define a family of harmonic mappings on the unit disk whose images are rotationally symmetric rosettes with $n$ cusps or n nodes, where $n \ge 3$. These mappings are analogous to the $n$-cusped hypocycloid, but are modified by Gauss hypergeometric factors, both in the analytic and co-analytic parts. Relative rotations by an angle $β$ of the analytic and anti-analytic parts lead to graphs that have cyclic, and in some cases dihedral symmetry of order $n$. While the graphs for different $β$ can be dissimilar, the cusps are aligned along axes that are independent of $β$. For certain isolated values of $β$, the boundary function is continuous with arcs of constancy, and has nodes of interior angle $π/2-π/n$.
