Journal Articles Pacific Journal of Mathematics Year : 2006

An optimal systolic inequality for CAT(0) metrics in genus two

Abstract

We prove an optimal systolic inequality for CAT(0) metrics on a genus 2 surface. We use a Voronoi cell technique, introduced by C. Bavard in the hyperbolic context. The equality is saturated by a flat singular metric in the conformal class defined by the smooth completion of the curve y^2 = x^5 - x. Thus, among all CAT(0) metrics, the one with the best systolic ratio is composed of six flat regular octagons centered at the Weierstrass points of the Bolza surface.

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hal-04328720 , version 1 (07-12-2023)

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Mikhail Katz, Stéphane Sabourau. An optimal systolic inequality for CAT(0) metrics in genus two. Pacific Journal of Mathematics, 2006, 227 (1), pp.95-107. ⟨10.2140/pjm.2006.227.95⟩. ⟨hal-04328720⟩
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