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math.DG2005
An optimal systolic inequality for CAT(0) metrics in genus two
Mikhail G. Katz, Stephane Sabourau
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…
math.DG2004★ 1 cited
Entropy of systolically extremal surfaces and asymptotic bounds
Mikhail G. Katz, Stephane Sabourau
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, t…