Kohn-Rossi cohomology and nonexistence of CR morphisms between compact strongly pseudoconvex CR manifolds (Q1732045)

One of the interesting questions in CR geometry is the existence of non-constant CR morphisms between strongly pseudo-convex CR manifolds of even dimensions. In this paper, and following their previous works, the authors consider this question. Their former results in this setting answer it in some considerable cases in particular in terms of the so-called plurigeneras of CR manifolds. However, there is no known method to compute these invariants just in terms of the known datum of CR manifolds. Accordingly, in this paper, the authors endeavor to classify the problem by means of the so-called Kohn-Rossi cohomology of CR manifolds. In particular, they show that for two strongly pseudo-convex CR manifolds $X_1$ and $X_2$ of dimension $2n-1$, if \[ \dim H^{p,q}_{KR}(X_1)< \dim H^{p,q}_{KR}(X_2) \] for any $(p,q)$ with $1\leq q\leq n-2$, then there is no non-constant CR morphism from $X_1$ to $X_2$.