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

作　　者：Fei LIU Fang WANG 

机构地区：[1]College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao 266590,P.R.China [2]School of Mathematical Sciences,Capital Normal University,Beijing 100048,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2021年第8期1219-1228,共10页数学学报（英文版）

基　　金：supported by Natural Science Foundation of Shandong Province(Grant No.ZR2020MA017);partially supported by NSFC(Grant No.11871045).

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 T^(1)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.

关 键 词：Geodesic flows Patterson-Sullivan measure Knieper measure 

分 类 号：O186.1[理学—数学]