Entropy of systolically extremal surfaces and asymptotic bounds

Mikhail G. Katz; Stephane Sabourau

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arXiv · math/0410312

Entropy of systolically extremal surfaces and asymptotic bounds

Mikhail G. Katz·Stephane Sabourau

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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.

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BibTeX RIS

Mikhail G. Katz, Stephane Sabourau. 2004-12-17. Entropy of systolically extremal surfaces and asymptotic bounds. https://arxiv.org/abs/math/0410312

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