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Minimal entropy rigidity for Finsler manifolds of negative flag curvature

Published online by Cambridge University Press:  07 March 2001

JEFF BOLAND  and
FLORENCE NEWBERGER
JEFF BOLAND
Affiliation:
Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada (e-mail: bolandj@icarus.math.mcmaster.ca)
FLORENCE NEWBERGER
Affiliation:
Department of Mathematics, Pennsylvania State University, State College, PA, USA (e-mail: fan@math.psu.edu)
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Abstract

We define a normalized entropy functional for compact Finsler manifolds of negative flag curvature. Using the method of Besson, Courtois, and Gallot, we show that among all such manifolds that are homotopy equivalent to a compact, Riemannian, locally symmetric manifold of negative curvature, the entropy functional is minimized precisely on the locally symmetric manifold.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 1 , February 2001 , pp. 13 - 23
Copyright
© 2001 Cambridge University Press

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