Geodesic
On the existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds
Sbornik. Mathematics, Tome 56 (1987) no. 2, pp. 349-358 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Riemannian manifold is said to be parabolic if there does no exist a positive fundamental solution of the Laplace equation on it. The purpose of this article is to obtain geometric conditions, both necessary and sufficient, for a manifold to be parabolic. Bibliography: 11 titles. 
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     title = {On the existence of positive fundamental solutions of the {Laplace} equation on {Riemannian} manifolds},
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A. A. Grigor'yan. On the existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds. Sbornik. Mathematics, Tome 56 (1987) no. 2, pp. 349-358. http://geodesic.mathdoc.fr/item/SM_1987_56_2_a4/

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