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- Brookhaven National LaboratoryUS10 papers
- Harvard UniversityUS10 papers
- Institute of Radio AstronomyUA8 papers
- Hebrew University of JerusalemIL3 papers
- Steklov Mathematical InstituteRU3 papers
- Tel Aviv UniversityIL3 papers
- University of ChicagoUS3 papers
- University of FloridaUS3 papers
- University of Notre DameUS3 papers
- Compugen (Israel)IL2 papers
- Harvard University PressUS2 papers
- Technion – Israel Institute of TechnologyIL2 papers
5 papers · 1 filter
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…
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…
Filling area conjecture and ovalless real hyperelliptic surfaces
Victor Bangert, Christopher Croke, Sergei V. Ivanov +1
We prove the filling area conjecture in the hyperelliptic case. In particular, we establish the conjecture for all genus 1 fillings of the circle, extending P. Pu's result in genus…