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arXiv · 1103.0211

Boundary behavior of the Kobayashi distance in pseudoconvex Reinhardt domains

Tomasz Warszawski
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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.

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Tomasz Warszawski. 2012-06-26. Boundary behavior of the Kobayashi distance in pseudoconvex Reinhardt domains. https://doi.org/10.1307/mmj%2F1347040260

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