On the Gromov hyperbolicity of convex domains in Cn
Complex Variables
2013-12-03 v1 Differential Geometry
Abstract
We give a necessary complex geometric condition for a bounded smooth convex domain in Cn, endowed with the Kobayashi distance, to be Gromov hyperbolic. More precisely, we prove that if a smooth bounded convex domain contains an analytic disk in its boundary, then the domain is not Gromov hyperbolic for the Kobayashi distance. We also provide examples of bounded smooth convex domains that are not strongly pseudoconvex but are Gromov hyperbolic.
Keywords
Cite
@article{arxiv.1312.0368,
title = {On the Gromov hyperbolicity of convex domains in Cn},
author = {Hervé Gaussier and Harish Seshadri},
journal= {arXiv preprint arXiv:1312.0368},
year = {2013}
}
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17 pages