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

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dc.creatorKatz, Mikhail G.
dc.creatorSabourau, Stephane
dc.date2005-01-02
dc.date2006-04-11
dc.date.accessioned2026-07-07T06:39:14Z
dc.date.available2026-07-07T06:39:14Z
dc.descriptionWe 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.
dc.description14 pages, 1 figure, to appear in Pacific J. Math
dc.identifierhttps://arxiv.org/abs/math/0501017
dc.identifierhttp://arxiv.org/abs/math/0501017
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101004
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.subjectMetric Geometry
dc.subject53C20, 53C23
dc.titleAn optimal systolic inequality for CAT(0) metrics in genus two
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