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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…
math.DG2004
Hyperelliptic surfaces are Loewner
Mikhail G. Katz, Stephane Sabourau
We prove that C. Loewner's inequality for the torus is satisfied by all hyperelliptic surfaces X, as well. We first construct the Loewner loops on the (mildly singular) companion t…