Let D be a simply connected plane domain and B the unit disk. The inner radius of D, , is defined by . Here Sf is the Schwarzian derivative of f, the hyperbolic density on D and . Domains for which the value of is known include disks, angular sectors and regular polygons, as well as certain classes of rectangles and equiangular hexagons. All of the mentioned domains except non-convex angular sectors have an interesting property in common, namely that , where h maps B conformally onto D. Because of the importance of this property for computing , we say that D is a Nehari disk if holds.¶This paper is devoted to the problem of characterizing Nehari disks. We give a necessary and sufficient condition for a domain to be a Nehari disk provided it is a regulated domain with convex corners.
Cite this article
L. Miller-Van Wieren, On Nehari disks and the inner radius. Comment. Math. Helv. 76 (2001), no. 2, pp. 183–199DOI 10.1007/PL00000377