Conformal capacities and extremal metrics (Q1816521)

For all non-compact Riemannian \(n\)-manifolds \(M\) the function \(\lambda_M: M\times M\to \overline {\mathbb{R}}_+\) is defined in [\textit{J. Ferrand}, C. R. Acad. Sci., Paris, Sér. I 318, No. 3, 213-216 (1994; Zbl 0794.53024)]. It is proved here that \(\lambda_M^{1/ (1-n)}\) satisfies the triangular inequality. This result includes a Vuorinen conjecture; it follows from an extension of a classical property of extremal functions to the case of condensers with unbounded boundary components.