Albuquerque, Paul Uniqueness of conformal densities and the semiflow of Weyl chambers. (English. Abridged French version) Zbl 0912.53035 C. R. Acad. Sci., Paris, Sér. I, Math. 326, No. 9, 1105-1110 (1998). Summary: Let \(X=G/K\) be a symmetric space of noncompact type and \(\Gamma\) a discrete “generic” subgroup of \(G\) with critical exponent \(\delta(\Gamma)\). We show that, if \(\Gamma\) is of divergence type, then there is a unique \(\Gamma\)-invariant conformal density of dimension \(\delta(\Gamma)\) (hence a Patterson-Sullivan density) on the set of regular elements of the geometric boundary of \(X\). This problem is directly related to the recurrence of the semiflow of Weyl chambers on \(X/\Gamma\). Cited in 1 Review MSC: 53C35 Differential geometry of symmetric spaces 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 53D25 Geodesic flows in symplectic geometry and contact geometry Keywords:discrete subgroup; symmetric space; divergence type; conformal density; geometric boundary; recurrence; semiflow of Weyl chambers PDFBibTeX XMLCite \textit{P. Albuquerque}, C. R. Acad. Sci., Paris, Sér. I, Math. 326, No. 9, 1105--1110 (1998; Zbl 0912.53035) Full Text: DOI