5 papers
Klein bottle and optimal systolic inequality for nonpositively curved surfaces
Mikhail G. Katz, Stephane Sabourau
We show that the systolic area of every nonpositively curved closed surface other than the torus is at least , with equality if and only if is isometric to a square flat…
An inequality for anti-self-polar polytopes
Mikhail G. Katz
We prove an inequality for the f-vectors of anti-self-polar polytopes conjectured by Katz in 1989. The proof uses Kalai's combinatorial inequality based on a result of Whiteley. Th…
On comass and stable systolic inequalities
James J. Hebda, Mikhail G. Katz
We study the maximum ratio of the Euclidean norm to the comass norm of p-covectors in Euclidean n-space and improve the known upper bound found in the standard references by Whitne…
Logarithmic systolic growth for hyperbolic surfaces in every genus
Mikhail G. Katz, Stephane Sabourau
More than thirty years ago, Brooks and Buser-Sarnak constructed sequences of closed hyperbolic surfaces with logarithmic systolic growth in the genus. Recently, Liu and Petri showe…
Nonpositively curved surfaces are Loewner
Mikhail G. Katz, Stephane Sabourau
We show that every closed nonpositively curved surface satisfies Loewner's systolic inequality. The proof relies on a combination of the Gauss-Bonnet formula with an averaging argu…