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MEAN-VALUE PROPERTY ON MANIFOLDS WITH MINIMAL HOROSPHERES

Part of: Global differential geometry

Published online by Cambridge University Press:  01 April 2008

LEONARD TODJIHOUNDE
LEONARD TODJIHOUNDE*
Affiliation:
Institut de Mathematiques et de Sciences Physiques, B.P. 613 Porto-Novo, Republique du Benin (email: leonardt@imsp-uac.org)
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Abstract

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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.

Keywords

mean-value propertyminimal horospheres

MSC classification

Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 2 , April 2008 , pp. 277 - 282
Copyright
Copyright © 2008 Australian Mathematical Society

References

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