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arXiv · 0803.0690

Loewner's torus inequality with isosystolic defect

Charles Horowitz·Karin Usadi Katz·Mikhail G. Katz
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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.

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Charles Horowitz, Karin Usadi Katz, Mikhail G. Katz. 2009-02-12. Loewner's torus inequality with isosystolic defect. https://arxiv.org/abs/0803.0690

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