Spherical means on compact locally symmetric spaces of non-positive curvature

Peyerimhoff, N.

Abstract

We consider spherical means of continuous functions on the unit tangent bundle of a compact, non-positively curved locally symmetric space and study their behavior as the radius tends to infinity. In dimension greater or equal to 2, we prove that spherical means converge to a probability measure of maximal entropy. This limit measure has an easy characterization in both geometric and algebraic terms. On our way we also derive a convergence result for horospherical means on compact locally symmetric spaces of noncompact type.

Citation

Peyerimhoff, N. (2006). Spherical means on compact locally symmetric spaces of non-positive curvature. Forum Mathematicum, 18(3), 391-417. https://doi.org/10.1515/forum.2006.022

• Journal Article Type: Article
• Publication Date: May 1, 2006
• Deposit Date: Feb 16, 2009
• Journal: Forum Mathematicum
• Print ISSN: 0933-7741
• Electronic ISSN: 1435-5337
• Publisher: De Gruyter
• Peer Reviewed: Peer Reviewed
• Volume: 18
• Issue: 3
• Pages: 391-417
• DOI: https://doi.org/10.1515/forum.2006.022
• Public URL: https://durham-repository.worktribe.com/output/1577418