English

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

R2 v1 2026-06-21T09:35:33.069Z