On the definition of the Virtanen property for Riemannian manifolds (Q1898250)

In our former paper [Duke Math. J. 67, No. 3, 589-625 (1992; Zbl 0764.53032)]\ we introduced a notion which we called the `Virtanen property' for Riemannian manifolds. The property is always fulfilled by two-dimensional Riemannian manifolds so that it often ensures the possibility of extending certain potential theoretic results valid for two-dimensional case to higher dimensions. The purpose of this paper is to give a new definition of the Virtanen property which is equivalent to but more understandable than that given in loc. cit.