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Keywords:
Poisson integral; Poisson kernel; Dirichlet problem; harmonic function; Riemannian manifold; hypergeometric function
Poisson integral; Poisson kernel; Dirichlet problem; harmonic function; Riemannian manifold; hypergeometric function
Summary:
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.
References:
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