On the Gromov Hyperbolicity of Convex Domains in \({\mathbb {C}}^n\)



We prove that if a \({\mathcal {C}}^\infty \)-smooth bounded convex domain in \({\mathbb {C}}^n\) contains a holomorphic disc in its boundary, then the domain is not Gromov hyperbolic for the Kobayashi distance. We also give examples of bounded smooth convex domains that are not strongly pseudoconvex but are Gromov hyperbolic.


Gromov hyperbolicity Kobayashi distance Convex domain 

Mathematics Subject Classification

32F45 32Q45 53C23 



We would like to thank the referee for valuable comments and suggestions that considerably improved the exposition.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Univ. Grenoble Alpes, CNRS, IFGrenobleFrance
  2. 2.Department of MathematicsIndian Institute of ScienceBangaloreIndia

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