Holomorphic mappings preserving Minkowski functionals

الأصل · EN

We show that the equality m₁(f(x))=m₂(g(x)) for x in a neighborhood of a point a remains valid for all x provided that f and g are open holomorphic maps, f(a)=g(a)=0 and m₁, m₂ are Minkowski functionals of bounded balanced domains. Moreover, a polynomial relation between f and g is obtained. Next we generalize these results to bounded quasi-balanced domains. Moreover, the main results of Ber-Piz and Bou are significantly extended and their proofs are essentially simplified.