Affine algebraic manifolds without dominant morphisms from euclidean spaces

E develop a method which in some cases enables us to establish the absence of dominant morphisms from Euclidean spaces into afiine algebraic manifolds which are hypersurfaces in Cⁿ. This approach shows that many of recently constructed smooth contractible hypersurfaces in Cⁿ, n ≥ 4, are not isomorphic to Euclidean spaces and cannot be used as counterexamples to the Zariski cancellation conjecture, to the Abhyankar-Sathaye conjecture, and to the problem of linearizing a C*-action on C³.