Domains in RnRn with conically accessible boundary

In this paper some characterizations and properties of domains in RnRn 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 αα-accessible domains of CNCN, 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.