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MEAN-VALUE PROPERTY ON MANIFOLDS WITH MINIMAL HOROSPHERES

  • LEONARD TODJIHOUNDE (a1)
Abstract

Let (M,g) be a non-compact and complete Riemannian manifold with minimal horospheres and infinite injectivity radius. In this paper we prove that bounded functions on (M,g) satisfying the mean-value property are constant. We thus extend a result of Ranjan and Shah [‘Harmonic manifolds with minimal horospheres’, J. Geom. Anal.12(4) (2002), 683–694] where they proved a similar result for bounded harmonic functions on harmonic manifolds with minimal horospheres.

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References
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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