Integral Geometric Properties of Non-compact Harmonic Spaces

Peyerimhoff, Norbert; Samiou, Evangelia

Abstract

On non-compact harmonic manifolds we prove that functions satisfying the mean value property for two generic radii must be harmonic. Moreover, functions with vanishing integrals over all spheres (or balls) of two generic radii must be identically zero. We also prove results about the Cheeger constant and the heat kernel.

Citation

Peyerimhoff, N., & Samiou, E. (2015). Integral Geometric Properties of Non-compact Harmonic Spaces. Journal of Geometric Analysis, 25(1), Article 122. https://doi.org/10.1007/s12220-013-9416-7

• Journal Article Type: Article
• Acceptance Date: Mar 11, 2013
• Online Publication Date: Apr 12, 2013
• Publication Date: Jan 1, 2015
• Deposit Date: Jan 6, 2016
• Publicly Available Date: Mar 30, 2016
• Journal: Journal of Geometric Analysis
• Print ISSN: 1050-6926
• Electronic ISSN: 1559-002X
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Issue: 1
• Article Number: 122
• DOI: https://doi.org/10.1007/s12220-013-9416-7
• Public URL: https://durham-repository.worktribe.com/output/1415542
• Related Public URLs: http://arxiv.org/pdf/1210.3957v1.pdf