On the maximum conjecture

We verify the maximum conjecture on the rigidity of totally nondegenerate model CR manifolds in the following two cases: (i) for all models of CR dimension one (ii) for the so-called full-models, namely those in which their associated symbol algebras are free CR. In particular, we discover that in each arbitrary CR dimension and length >= 3, there exists at least one totally nondegenerate model, enjoying this conjecture. Our proofs rely upon some recent results in the Tanaka theory of transitive prolongation of fundamental algebras.