A digression

An Observation on the Dirichlet Problem at Infinity in Riemannian Cones

“…We shall assume that is smooth, with if , and that and . When and thus M is a manifold, the conditions imposed on guarantee that the metric g can be extended, as a metric, smoothly up to the pole or vertex of M , as we shall refer to the equivalence class of (see [10]). It is usual to define the cone metric using , so our definition of a Riemannian cone is a bit more general.…”