On proper holomorphic self-maps of generalized complex ellipsoids

The purpose of this paper is to prove that every proper holomorphic self-mapping of a Reinhardt domain Ω in C ⁿ which is a generalization of a complex ellipsoid is biholomorphic. The main novelty of our result is that Ω is a domain in C ⁿ such that it is allowed to have a boundary point at which the Levi determinant has infinite order of vanishing.