Some remarks about Reinhardt domains in Cn

We show that, given a bounded Reinhardt domain D in C-n, there exists a hyperconvex domain Omega such that Omega contains D and every holomorphic function on a neighborhood of D extends to a neighborhood of Omega. As a consequence of this result, we recover an earlier result stating that every bounded fat Reinhardt domain having a Stein neighbourhoods basis must be hyperconvex. We also study the connection between the Caratheodory hyperbolicity of a Reinhardt domain and that of its envelope of holomorphy. We give an example of a Caratheodory hyperbolic Reinhardt domain in C-3, for which the envelope of holomorphy is not Caratheodory hyperbolic, and we show that no such example exists in C-2.