Margulis-Ruelle inequality for general manifolds
Gang Liao, Na Qiu
TL;DR
This paper extends the Margulis-Ruelle inequality to general Riemannian manifolds, including noncompact and boundary cases, demonstrating its validity under certain integrability conditions.
Contribution
It generalizes the inequality to broader classes of manifolds, expanding its applicability beyond compact cases.
Findings
The inequality holds for noncompact manifolds with boundary.
It is valid under specific integrability conditions.
The results unify the understanding of entropy and Lyapunov exponents on general manifolds.
Abstract
In this paper we investigate the Margulis-Ruelle inequality for general Riemannian manifolds (possibly noncompact and with boundary) and show that it always holds under integrable condition.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Analytic and geometric function theory · Mathematical Dynamics and Fractals