On the Area of Immersed Minimal Annuli in a Slab

We organize minimal annuli in a slab based on the winding number of the circles that foliate them and study the area of minimal annuli with given winding number. Specifically, we deduce some results regarding the convexity of the length function of corresponding level curves, and apply them to estimate the area of the annuli by comparing to the area of waist of covers of catenoids.