Entropy of systolically extremal surfaces and asymptotic bounds

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dc.creatorKatz, Mikhail G.
dc.creatorSabourau, Stephane
dc.date2004-10-13
dc.date2004-12-17
dc.date.accessioned2026-07-07T05:13:15Z
dc.date.available2026-07-07T05:13:15Z
dc.descriptionWe 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.
dc.description14 pages. Ergodic Theory and Dynamical Systems, to appear
dc.identifierhttps://arxiv.org/abs/math/0410312
dc.identifierhttp://arxiv.org/abs/math/0410312
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72876
dc.subjectDifferential Geometry
dc.subjectCombinatorics
dc.subjectDynamical Systems
dc.subjectGeometric Topology
dc.subjectMetric Geometry
dc.subject53C23
dc.titleEntropy of systolically extremal surfaces and asymptotic bounds
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