Mean-value property on manifolds with minimal horospheres

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Let (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 Society

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Differential Geometry, 53C21; 53C25

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http://salesiana.dossiersoluciones.com/handle/123456789/140725

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0710.4494
 http://arxiv.org/abs/0710.4494

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arXiv