Geodesic
Biharmonic Green domains in a Riemannian manifold
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 2, pp. 359-365.

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Let $R$ be a Riemannian manifold without a biharmonic Green function defined on it and $\Omega $ a domain in $R$. A necessary and sufficient condition is given for the existence of a biharmonic Green function on $\Omega $.
Classification : 31B30, 31C12
Keywords: biharmonic Green functions 
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     title = {Biharmonic {Green} domains in a {Riemannian} manifold},
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Othman, S. I.; Anandam, V. Biharmonic Green domains in a Riemannian manifold. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 2, pp. 359-365. http://geodesic.mathdoc.fr/item/CMUC_2003__44_2_a13/