Nonconstant CR morphisms betweenc compact strongly pseudoconvex CR manifolds and étale covering between resolutions of isolated singularities

Abstract

Strongly pseudoconvex CR manifolds are boundaries of Stein varieties with isolated normal singularities. We prove that any non- constant CR morphism between two $(2n−1)$-dimensional strongly pseudoconvex CR manifolds lying in an $n$-dimensional Stein variety with isolated singularities are necessarily a CR biholomorphism. As a corollary, we prove that any nonconstant self map of $(2n − 1)$-dimensional strongly pseudoconvex CR manifold is a CR automorphism. We also prove that a finite étale covering map between two resolutions of isolated normal singularities must be an isomorphism.