Linear growth and bounded geometry (Q1567090)

In [\textit{L. Funar and R. Grimaldi}, J. Math. Pures Appl. 76, 851-858 (1997; Zbl 0886.53036)] it was shown that a non-compact Riemannian manifold having bounded geometry and linear growth-type must have finite topology at infinity. In this paper, the author proves the converse by constructing, on an arbitrary non-compact manifold with finite topology at infinity, a complete Riemannian metric with bounded geometry and linear growth-type.