Commentarii Mathematici Helvetici

We give an estimate for the distance function related to the Kobayashi metric on a bounded strictly pseudoconvex domain with C 2-smooth boundary. Our formula relates the distance function on the domain with the Carnot-Carathéodory metric on the boundary. The estimate is precise up to a bounded additive term. As a corollary we conclude that the domain equipped with this distance function is hyperbolic in the sense of Gromov.

Nous reformulons un résultat récent de Arason et Elman en donnant une présentation très simple des puissances de l’idéal fondamental de l’anneau de Witt d’un corps de caractéristique ≠ 2.

Let $ \Gamma $ be a cocompact Fuchsian group. We calculate the lower algebraic K-theory of the integral group ring $ {\Bbb Z} \Gamma $ and find an explicit formula for $ {\rm K}_{i}({\Bbb Z}\Gamma),\,i \le 1 $ , in terms of the lower K-groups of maximal finite cyclic subgroups of $ \Gamma $ .