Mean-value property on manifolds with minimal horospheres

2007/10/24 by Léonard Todjihounde, Leonard Todjihounde, Todjihounde, Leonard
Mathematics · #53C21 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #math.DG #msc:53C21 #msc:53C25

paper · pdf · doi:10.48550/arxiv.0710.4494

A slightly edited version will appear in Journal of the Australian Mathematical Society

arxiv created 2007/10/24 · openalex publication_date 2007/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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