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

被引：0

作者：

Liu, Fei ^{[1
]}

Wang, Fang ^{[2
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[2] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2021年 / 37卷 / 08期

关键词：

Geodesic flows; Patterson-Sullivan measure; Knieper measure; GEODESIC-FLOWS; MAXIMAL ENTROPY; GEOMETRY;

D O I：

10.1007/s10114-021-0465-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 (TM)-M-1 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.

引用

页码：1219 / 1228

页数：10

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