30 citations · 199 across the 25 of their papers we have counts for
5 papers · 1 filter
Bolza quaternion order and asymptotics of systoles along congruence subgroups
Karin Katz, Mikhail Katz, Michael Schein +1
We give a detailed description of the arithmetic Fuchsian group of the Bolza surface and the associated quaternion order. This description enables us to show that the corresponding…
Relative systoles of relative-essential 2-complexes
Karin U. Katz, Mikhail G. Katz, Stephane Sabourau +2
We prove a systolic inequality for the phi-relative 1-systole of a phi-essential 2-complex, where phi is a homomorphism from the fundamental group of the complex, to a finitely pre…
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…
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…