Topologies defined by some invariant pseudodistances
In this article, estimates of the hyperbolic and Carathéodory distances in domains , n ≥ 1, are obtained. They are equally valid for the Kobayashi distance.
It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with -smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for any finitely connected planar domain.