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

Mikhail G. Katz; Stephane Sabourau

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

Mikhail G. Katz·Stephane Sabourau

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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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BibTeX RIS

Mikhail G. Katz, Stephane Sabourau. 2006-04-11. An optimal systolic inequality for CAT(0) metrics in genus two. https://arxiv.org/abs/math/0501017

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