Boundary behavior of the Kobayashi distance in pseudoconvex Reinhardt domains

Abstract

We prove that the Kobayashi distance near boundary of a pseudoconvex Reinhardt domain $D$ increases asymptotically at most like $-\log d_D+C$. Moreover, for boundary points from $\text{int}\bar{D}$ the growth does not exceed $1/2\log (-\log d_D)+C$. The lower estimate by $-1/2\log d_D+C$ is obtained under additional assumptions of ${\mathcal{C}}^1$-smoothness of a domain and a non-tangential convergence.

16 pages. To appear in Mich. Math. J

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