10 citations · 16 across the 4 of their papers we have counts for
4 papers
Bi-Lipschitz approximation by finite-dimensional imbeddings
Karin Usadi Katz, Mikhail G. Katz
We show that the Kuratowski imbedding of a Riemannian manifold in L^\infty, exploited in Gromov's proof of the systolic inequality for essential manifolds, admits an approximation…
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…
A strict non-standard inequality .999... < 1
Karin Usadi Katz, Mikhail G. Katz
Is .999... equal to 1? Lightstone's decimal expansions yield an infinity of numbers in [0,1] whose expansion starts with an unbounded number of digits "9". We present some non-stan…
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…