Reduced polygons in the hyperbolic plane.

For a hyperplane H supporting a convex body C in the hyperbolic space H d , we define the width of C determined by H as the distance between H and a most distant ultraparallel hyperplane supporting C. The minimum width of C over all supporting H is called the thickness Δ (C) of C. A convex body R ⊂ H d is said to be reduced if Δ (Z) < Δ (R) for every convex body Z properly contained in R. We describe a class of reduced polygons in H 2 and present some properties of them. In particular, we estimate their diameters in terms of their thicknesses. [ABSTRACT FROM AUTHOR]