Boundary dimension in negatively curved spaces
The paper deals with the so-called Gromov hyperbolic (negatively curved) spaces \(X\) which generalize the most important case of negatively curved groups, see \textit{M. Gromov} [Essays in group theory, Publ., Math. Sci. Res. Inst. 8, 75-263 (1987; Zbl 0634.20015)]. Gromov's condition on \(X\) to have finite-dimensional boundary \(\partial X\) is that \(X\) be a simplicial graph with bounded valence and unit length edges (which cover the case of the Cayley graph of a hyperbolic group, see also Prop. 6.2 in \textit{E. Ghys} and \textit{P. de la Harpe} [Sur les groupes hyperboliques d'après Mikhael Gromov, Prog. Math. 83, Boston, MA: Birkhäuser (1990; Zbl 0731.20025)]. The author gives a more general result which implies that such \(X\) with a cocompact isometry group action always has finite-dimensional boundary (the author's usage compact does not imply Hausdorff). As another result, the author gives an example of a negatively curved space \(X\) with infinite-dimensional boundary.
scientific article; zbMATH DE number 806290