Gears, pregears and related domains

被引：2
|
作者：
Brown, Philip R. [1 ]
Porter, R. Michael [2 ]
机构：
[1] Texas A&M Univ, Dept Gen Acad, Galveston, TX 77553 USA
[2] CINVESTAV IPN, Dept Matemat, Santiago De Queretaro 76000, Mexico
来源：
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2016年 / 61卷 / 01期
关键词：
conformal mapping; accessory parameter; Schwarzian derivative; gearlike domain; conformal modulus; topological quadrilateral; Primary: 30C30; Secondary: 30C20; 33E05; CIRCULAR QUADRILATERALS; GEARLIKE DOMAINS;
D O I：
10.1080/17476933.2015.1057715
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study conformal mappings from the unit disc to one-toothed gear-shaped planar domains from the point of view of the Schwarzian derivative. Gear-shaped (or gearlike) domains fit into a more general category of domains we call pregears (images of gears under Mobius transformations), which aid in the study of the conformal mappings for gears and which we also describe in detail. Such domains being bounded by arcs of circles, the Schwarzian derivative of the Riemann mapping is known to be a rational function of a specific form. One accessory parameter of these mappings is naturally related to the conformal modulus of the gear (or pregear) and we prove several qualitative results relating it to the principal remaining accessory parameter. The corresponding region of univalence (parameters for which the rational function is the Schwarzian derivative of a conformal mapping) is determined precisely.
引用
收藏
页码：89 / 103
页数：15
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