Closed polar sets in a Riemannian manifold
This paper is concerned with a characterization of polar sets in Riemann manifolds. More precisely, the authors establish that a subset \(E\) of a parabolic Riemannian manifold \(R\) is polar if and only if there exists a harmonic function \(u\) on \(R\setminus E\) whose limit at any point of \(\partial(R\setminus E)\) is infinity. In case the Riemannian manifold is of hyperbolic type, the above characterization is also equivalent to the existence of a positive harmonic function \(u\) having the above property.
scientific article; zbMATH DE number 5657225