Abstract. Let M0 be a compact, regular q-pseudoconcave compact CR submanifold of a complex manifold G and B- a holomorphic vector bundle on G such that dim Hr () M0, B ∣ = 0 for some M fixed r < q. We prove a global homotopy formula with Ck estimates for r-cohomology of B on arbitrary CR submanifold M close enough to M0. 1. Introduction. Let M be a compact generic CR submanifold in a complex n- dimensional manifold G, i.e. for any z ∈ M there exist a neighborhood V ∋ z in G and smooth real valued functions on V such tha
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