A short proof to the rigidity of volume entropy

Gang Liu

doi:10.4310/MRL.2011.v18.n1.a11

A short proof to the rigidity of volume entropy

Gang Liu^*

^*Corresponding author for this work

University of Minnesota Twin Cities

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In this note we give a short proof to the rigidity of volume entropy. The result says that for a closed manifold with Ricci curvature bounded from below, if the universal cover has maximal volume entropy, then it is the space form. This theorem was first proved by F. Ledrappier and X. Wang in [1].

Original language	English
Pages (from-to)	151-153
Number of pages	3
Journal	Mathematical Research Letters
Volume	18
Issue number	1
DOIs	https://doi.org/10.4310/MRL.2011.v18.n1.a11
State	Published - Jan 2011
Externally published	Yes

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10.4310/MRL.2011.v18.n1.a11

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title = "A short proof to the rigidity of volume entropy",

abstract = "In this note we give a short proof to the rigidity of volume entropy. The result says that for a closed manifold with Ricci curvature bounded from below, if the universal cover has maximal volume entropy, then it is the space form. This theorem was first proved by F. Ledrappier and X. Wang in [1].",

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AB - In this note we give a short proof to the rigidity of volume entropy. The result says that for a closed manifold with Ricci curvature bounded from below, if the universal cover has maximal volume entropy, then it is the space form. This theorem was first proved by F. Ledrappier and X. Wang in [1].

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JO - Mathematical Research Letters

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A short proof to the rigidity of volume entropy

Abstract

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