Loewner's torus inequality with isosystolic defect

Abstract

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 conformal factor of the metric g with respect to the flat metric of unit area in the conformal class of g.

15 pages, 1 figure

References in corpus (2)

• Hyperellipticity and Klein bottle companionship in systolic geometry
• Cayley 4-form, comass, and triality isomorphisms