KOHN-ROSSI COHOMOLOGY AND NONEXISTENCE OF CR MORPHISMS BETWEEN COMPACT STRONGLY PSEUDOCONVEX CR MANIFOLDS

One of the fundamental questions in CR geometry is: Given two strongly pseudoconvex CR manifolds X-1 and X-2 of dimension 2n-1, is there a non-constant CR morphism between them? In this paper, we use Kohn-Rossi cohomology to show the non-existence of non-constant CR morphism between such two CR manifolds. Specifically, if dim H-KR(p,q) (X-1) < dim H-KR(p,q) (X-2) for any (p, q) with 1 <= q <= n - 2, then there is no non-constant CR morphism from X-1 to X-2.