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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… Click to show full abstract
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 T1M 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.
Keywords:
non positive;
manifolds non;
knieper measure;
non compact;
positive curvature
Journal Title: Acta Mathematica Sinica, English Series
Year Published: 2021
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Journal Title: Acta Mathematica Sinica, English Series
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!