Mean-value property on manifolds with minimal horospheres
Differential Geometry
2007-10-25 v1
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.
Keywords
Cite
@article{arxiv.0710.4494,
title = {Mean-value property on manifolds with minimal horospheres},
author = {Leonard Todjihounde},
journal= {arXiv preprint arXiv:0710.4494},
year = {2007}
}
Comments
A slightly edited version will appear in Journal of the Australian Mathematical Society