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MEAN-VALUE PROPERTY ON MANIFOLDS WITH MINIMAL HOROSPHERES
Published online by Cambridge University Press: 01 April 2008
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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- Copyright © 2008 Australian Mathematical Society
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