Geodesic
The Poisson integral for a ball in spaces of constant curvature
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 3, pp. 437-460

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We present explicit expressions of the Poisson kernels for geodesic balls in the higher dimensional spheres and real hyperbolic spaces. As a consequence, the Dirichlet problem for the projective space is explicitly solved. Comparison of different expressions for the same Poisson kernel lead to interesting identities concerning special functions.
Classification : 31C12, 33C90, 35J25
Keywords: Poisson integral; Poisson kernel; Dirichlet problem; harmonic function; Riemannian manifold; hypergeometric function 
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     title = {The {Poisson} integral for a ball in spaces of constant curvature},
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Symeonidis, Eleutherius. The Poisson integral for a ball in spaces of constant curvature. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 3, pp. 437-460. http://geodesic.mathdoc.fr/item/CMUC_2003__44_3_a4/