Domains in with conically accessible boundary

In this paper some characterizations and properties of domains in R n with boundary accessible externally by some circular cones are given. It is shown that the boundary of such domains is also conically accessible from the interior. It is also characterized α -accessible domains of C N , which are biholomorphically equivalent to the open Euclidean ball. The paper is also a continuation of a concept of V.V. Starkov (2011)  [13] and refers to papers of D.A. Brannan and W.E. Kirwan (1969)  [3], W. Ma and D. Minda (1991)  [10], J. Stankiewicz (1966)  [11], and T. Sugawa (2005)  [15] connected with a planar case.