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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…
Lusternik-Schnirelmann category and systolic category of low dimensional manifolds
Mikhail G. Katz, Yuli B. Rudyak
We show that the geometry of a Riemannian manifold (M,g) is sensitive to the apparently purely homotopy-theoretic invariant of M known as the Lusternik-Schnirelmann category, denot…
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…
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…
Boundary case of equality in optimal Loewner-type inequalities
Victor Bangert, Christopher Croke, Sergei V. Ivanov +1
We prove certain optimal systolic inequalities for a closed Riemannian manifold (X,g), depending on a pair of parameters, n and b. Here n is the dimension of X, while b is its firs…
Generalized degree and optimal Loewner-type inequalities
Sergei V. Ivanov, Mikhail G. Katz
We generalize optimal inequalities of C. Loewner and M. Gromov, by proving lower bounds for the total volume in terms of the homotopy systole and the stable systole. Our main tool…