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