Mathematical Research Letters

Volume 18 (2011)

Number 1

A short proof to the rigidity of volume entropy

Pages: 151 – 153

DOI: http://dx.doi.org/10.4310/MRL.2011.v18.n1.a11

Author

Gang Liu (Department of Mathematics, University of Minnesota, Minneapolis, MN 55455)

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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