Loewner's torus inequality with isosystolic defect

Details Loewner's torus inequality with isosystolic defect Loewner's torus inequality with isosystolic defect

2008-03-05

arxiv.org/abs/0803.0690v2

Mathematics

Differential Geometry

15 pages, 1 figure

Scientific paper

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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