Spherical functions and conformal densities on spherically symmetric $CAT(-1)$-spaces

@article{Coornaert1999SphericalFA,
  title={Spherical functions and conformal densities on spherically symmetric \$CAT(-1)\$-spaces},
  author={Michel Coornaert and Athanase Papadopoulos},
  journal={Transactions of the American Mathematical Society},
  year={1999},
  volume={351},
  pages={2745-2762}
}
Let X be a CAT (−1)-space which is spherically symmetric around some point x0 ∈ X and whose boundary has finite positive s−dimensional Hausdorff measure. Let μ = (μx)x∈X be a conformal density of dimension d > s/2 on ∂X. We prove that μx0 is a weak limit of measures supported on spheres centered at x0. These measures are expressed in terms of the total mass function of μ and of the d−dimensional spherical function on X. In particular, this result proves that μ is entirely determined by its… Expand
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