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Mathematics > Differential Geometry

arXiv:0710.4494 (math)
[Submitted on 24 Oct 2007]

Title:Mean-value property on manifolds with minimal horospheres

Authors: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.
Comments: A slightly edited version will appear in Journal of the Australian Mathematical Society
Subjects: Differential Geometry (math.DG)
MSC classes: 53C21; 53C25
Cite as: arXiv:0710.4494 [math.DG]
  (or arXiv:0710.4494v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.4494

Submission history

From: Leonard Todjihounde Prof. [view email]
[v1] Wed, 24 Oct 2007 15:18:07 UTC (4 KB)
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