Mean-value property on manifolds with minimal horospheres

Leonard Todjihounde

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arXiv · 0710.4494

Mean-value property on manifolds with minimal horospheres

Leonard Todjihounde

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Abstract

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.

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BibTeX RIS

Leonard Todjihounde. 2007-10-24. Mean-value property on manifolds with minimal horospheres. https://arxiv.org/abs/0710.4494

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