Gromov hyperbolicity and the Kobayashi metric on convex domains of finite type (Q303619)

The author answers a question that appeared in [\textit{H. Gaussier} and \textit{H. Seshadri}, ``On the Gromov hyperbolicity of convex domains in \(\mathbb{C}^n\)'', Preprint, \url{arXiv:1312.0368}]; namely, he proves that if \(\Omega\) is a bounded convex set with \(C^\infty\) boundary, then \((\Omega , d_\Omega )\) is Gromov hyperbolic if and only if \(\Omega\) has finite type in the sense of D'Angelo. Here, \(d_\Omega \) denotes the Kobayashi pseudo-distance. He also shows that the Gromov boundary can be identified with the topological boundary \(\partial \Omega\).