Cartan-decomposition subgroups of SU.
Traitant la série de Poincaré d’un groupe discret d’isométries en courbure négative comme un noyau de Green, on établit une théorie du potentiel assez comparable à la théorie classique pour affirmer un parallèle entre densités conformes à la Patterson-Sullivan et densités harmoniques, et notamment définir une frontière de Martin où les densités ergodiques forment la partie minimale, et enfin l’identifier géométriquement sous hypothèse d’hyperbolicité.
We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.
Let be a -adic field, and let endowed with the Haar measure determined by giving a maximal compact subgroup measure . Let denote the number of conjugacy classes of arithmetic lattices in with co-volume bounded by . We show that under the assumption that does not contain the element , where denotes the -th root of unity over , we have where denotes the order of the residue field of .
This survey on crystallographic groups, geometric structures on Lie groups and associated algebraic structures is based on a lecture given in the Ostrava research seminar in .