The Journal of Geometric Analysis

, Volume 26, Issue 1, pp 616–629 | Cite as

Lower Bounds on the Kobayashi Metric Near a Point of Infinite Type

  • Tran Vu Khanh


Under a potential-theoretical hypothesis named f-property which holds for all pseudoconvex domains of finite type and many examples of infinite type, we give a new method for constructing a family of bumping functions and hence plurisubharmonic peak functions with good estimates. The rate of lower bounds on the Kobayashi metric follows by the estimates of peak functions. The application to the continuous extendibility of proper holomorphic maps is given.


Kobayashi metric Proper holomorphic map Finite and infinite type 

Mathematics Subject Classification

Primary 32F45 32H35 



This article was written while the author was a visiting member at the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank this institution for its hospitality and support. He is also extremely grateful for the support given by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01–2012.16.


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Authors and Affiliations

  1. 1.School of Mathematics and Applied StatisticsUniversity of WollongongWollongongAustralia
  2. 2.Tan Tao UniversityTan Duc e-cityVietnam

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