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Let (M,g) be a non-compact and complete Riemannian manifold with minimalhorospheres and infinite injectivity radius. We prove that bounded functions on(M,g) satisfying the mean-value property are constant. We extend thus a resultof A. Ranjan and H. Shah who proved a similar result for bounded harmonicfunctions on harmonic manifolds with minimal horospheres.

Mean-value property on manifolds with minimal horospheres