Abstract

Abstract. We study the set where the so-called Bergman representative coordinates (or Bergman functions) form an immersion. We provide an estimate of the size of a maximal geodesic ball with respect to the Bergman metric, contained in this set. By concrete examples we show that these estimates are the best possible. Bergman representative coordinates were introduced by Bergman in [2] as a tool in his program of generalizing the Riemann mapping theorem to C n,n> 1. Their usefulness is based (among others) on the fact that biholomorphic mappings become linear when represented in these coordinates (See e.g., [12]).

Citations