Gears, pregears and related domains
Gears, pregears and related domains
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 Möbius transformations), which aid in the study of the …