2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140725Let (M,g) be a non-compact and complete Riemannian manifold with minimal horospheres and infinite injectivity radius. We prove that bounded functions on (M,g) satisfying the mean-value property are constant. We extend thus a result of A. Ranjan and H. Shah who proved a similar result for bounded harmonic functions on harmonic manifolds with minimal horospheres.A slightly edited version will appear in Journal of the Australian Mathematical SocietyDifferential Geometry53C21; 53C25text