The Uniqueness of Knieper Measure on Non-compact Rank 1 Manifolds of Non-positive Curvature

• 作者: Fei LIU Fang WANG
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（8）
• 页码范围: 1219-1228
• 页数: 10页
• 语种: 英文

摘要

We study the Knieper measures of the geodesic flows on non-compact rank 1 manifolds of non-positive curvature.We construct the Busemann density on the ideal boundary,and prove that if there is a Knieper measure on T1 M with finite total mass,then the Knieper measure is unique,up to a scalar multiple.Our result partially extends Paulin-Pollicott-Shapira's work on the uniqueness of finite Gibbs measure of geodesic flows on negatively curved non-compact manifolds to non-compact manifolds of non-positive curvature.