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math.DG2026
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…
math.DG2024
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…
math.DG2024
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…