Harmonic mappings onto R-convex domains

Abstract

The plane domain D is called R-convex if D contains each compact set bounded by two shortest sub-arcs of the radius R with endpoints w 1 , w 2 ∈ D, |w 1 −w 2 | 2R. In this paper, we prove the conditions of R-convexity for images of disks under harmonic sense preserving functions. The coefficient bounds for harmonic mappings of the unit disk onto R-convex domains are obtained.