One of fundamental questions in CR geometry ask:
Given two strongly pseudoconvex CR manifolds $X_1$ and $X_2$ of dimension $n-1$, determine whether there is a non-constant CR morphism between them. In this lecture we use Kohn-Rossi cohomology to show the non-existence of non-constant CR morphism between such two CR manifolds. Specifically, we show that there is no non-constant CR morphism from $X_1$ to $X_2$ if $\dim H^{p,q}_{KR} (X_1) < \dim H^{p,q}_{KR}(X_2)$ for any $(p,q)$ with $0 < q < n-1$.