TL;DR
This paper investigates the conditions under which Bergman representative coordinates form an immersion, providing optimal estimates for the size of maximal geodesic balls in the Bergman metric where this occurs.
Contribution
It offers new bounds on the size of regions where Bergman coordinates are immersive and demonstrates their optimality through concrete examples.
Findings
Optimal estimates for maximal geodesic balls in Bergman metric
Examples showing the sharpness of these estimates
Insights into the immersion properties of Bergman coordinates
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.
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