摘要
Let P and B be a polydisc and a ball in C^n respectively. Poincaré first pointed out that P was not equivalent analytically to B. Simha gave a new proof in terms of the Schwarz lemma in 1976. In this letter, we shall give another proof for this fact by using a property of the convex mappings on polydisc. Theorem. P is not equivalent analytically to B. Proof. If they were equivalent analytically, then there would exist an analytic and univalent mapping f which maps P onto B, i.e. f(P)=B. Let f(0)=0. Since B is a convex domain, by a theorem of Suffridge, there is a nonsingular matrix T, such
