DOI: 10.1307/mmj/1347040260
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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 intD 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 C 1 -smoothness of a domain and a non-tangential convergence.2010 Mathematics Subject Classification. Primary: 32F45. Secondary: 32A07.