Let F denote the class of all functions univalent in the unit disk and convex in the direction of the real axis. In the paper we discuss the functions of the class F which are n-fold symmetric, where n is positive even integer. For the class of such functions we find the Koebe set as well as the covering set, i.e. T f2F f ðDÞ and S f2F f ðDÞ. Moreover, the Koebe constant and the covering consta...

The critical curve C on which Im τ̂ = 0, τ̂ = aD/a, determines hyperbolic domains whose Poincaré metric is constructed in terms of aD and a. We describe C in a parametric form related to a Schwarzian equation and prove new relations for N = 2 Super SU(2) Yang-Mills. In particular, using the Koebe 1/4-theorem and Schwarz’s lemma, we obtain inequalities involving u, aD and a, which seem related to ...

We prove that every planar graph with maximum degree three has a planar drawing in which the edges are drawn as circular arcs that meet at equal angles around every vertex. Our construction is based on the Koebe–Thurston–Andreev circle packing theorem, and uses a novel type of Voronoi diagram for circle packings that is invariant under Möbius transformations, defined using three-dimensional hyp...