Entropy of systolically extremal surfaces and asymptotic bounds
Differential Geometry
2007-05-23 v2 Combinatorics
Dynamical Systems
Geometric Topology
Metric Geometry
Abstract
We find an upper bound for the entropy of a systolically extremal surface, in terms of its systole. We combine the upper bound with A. Katok's lower bound in terms of the volume, to obtain a simpler alternative proof of M. Gromov's asymptotic estimate for the optimal systolic ratio of surfaces of large genus. Furthermore, we improve the multiplicative constant in Gromov's theorem. We show that every surface of genus at least 20 is Loewner. Finally, we relate, in higher dimension, the isoembolic ratio to the minimal entropy.
Keywords
Cite
@article{arxiv.math/0410312,
title = {Entropy of systolically extremal surfaces and asymptotic bounds},
author = {Mikhail G. Katz and Stephane Sabourau},
journal= {arXiv preprint arXiv:math/0410312},
year = {2007}
}
Comments
14 pages. Ergodic Theory and Dynamical Systems, to appear