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Eleutherius Symeonidis 6DA 2EII EJACH= BH = >= E IF=?AI B ?IJ=J ?KHL=JKHA

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Eleutherius Symeonidis

The Poisson integral for a ball in spaces of constant curvature

Comment.Math.Univ.Carolinae 44,3 (2003) 437-460.

Abstract: 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.

Keywords: Poisson integral, Poisson kernel, Dirichlet problem, harmonic function, Riemannian manifold, hypergeometric function

AMS Subject Classification: Primary 31C12, 35J25; Secondary 33C90

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