30 citations · 199 across the 25 of their papers we have counts for
Showing 2008 · math.DGShow all
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math.DG2008★ 10 cited
Hyperellipticity and Klein bottle companionship in systolic geometry
Karin Usadi Katz, Mikhail G. Katz
Given a hyperelliptic Klein surface, we construct companion Klein bottles. Bavard's short loops on companion bottles are studied in relation to the surface to improve an inequality…
math.DG2008★ 2 cited
Loewner's torus inequality with isosystolic defect
Charles Horowitz, Karin Usadi Katz, Mikhail G. Katz
We show that Bonnesen's isoperimetic defect has a systolic analog for Loewner's torus inequality. The isosystolic defect is expressed in terms of the probabilistic variance of the…