Bounds for Invariant Distances on Pseudoconvex Levi Corank One Domains and Applications

The Kobayashi balls of ( $${\mathbb {C}}$$ C -)convex domains

“…The weakly pseudoconvex finite type case in C 2 , as well as the convex finite type case in C n , are treated in [6,Propositions 8.8 and 8.9] as byproducts of long considerations. The strongly pseudoconvex case in C n and the weakly pseudoconvex finite type in C 2 are particular cases of the pseudoconvex Levi corank one case which is considered in [3,Theorem 1.3]. The behavior of the Kobayashi balls in all the mentioned results is given in 2010 Mathematics Subject Classification.…”

“…), where kob D (q, r) is the Kobayashi ball {z ∈ D : k(q, z) < r} and D(p, r) = {z ∈ C : |z − p| < r}. By [4, Lemma 3.10], the sizes of these polydiscs are comparable (in terms of small/big constant depending on D) with the sizes of polydiscs in [3,6] arising from the Levi geometry of the boundary. Thus Theorem 1 extends [6, Propositions 8.9].…”