Hadamard spaces with isolated flats. (With an appendix written jointly with Mohamad Hindawi).
Harmonic measures versus quasiconformal measures for hyperbolic groups
We establish a dimension formula for the harmonic measure of a finitely supported and symmetric random walk on a hyperbolic group. We also characterize random walks for which this dimension is maximal. Our approach is based on the Green metric, a metric which provides a geometric point of view on random walks and, in particular, which allows us to interpret harmonic measures as quasiconformal measures on the boundary of the group.
Hyperbolic groups with low-dimensional boundary
Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions
We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature is “thin”, namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as Vinberg’s theory of hyperbolic reflection groups. The criterion is shown to be robust for showing that many hyperbolic hypergeometric groups for are thin.
Hyperbolicity of one-relator groups.