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Entropy and systoles on surfaces

Published online by Cambridge University Press:  26 July 2006

STÉPHANE SABOURAU
STÉPHANE SABOURAU
Affiliation:
Laboratoire de Mathématiques et Physique Théorique, Université de Tours, Parc de Grandmont, 37400 Tours, France (e-mail: [email protected]) and Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6395, USA
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Abstract

We show that the volume entropy of surfaces with unit systole is bounded from above by a constant which does not depend on the metric, which answers a question raised by A. Katok. This upper bound follows from a comparison between the geometric and algebraic lengths on the fundamental groups of surfaces.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 5 , October 2006 , pp. 1653 - 1669
Copyright
2006 Cambridge University Press

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