Loewner's torus inequality with isosystolic defect
Differential Geometry
2009-02-12 v2 Analysis of PDEs
Complex Variables
Metric Geometry
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.
Keywords
Cite
@article{arxiv.0803.0690,
title = {Loewner's torus inequality with isosystolic defect},
author = {Charles Horowitz and Karin Usadi Katz and Mikhail G. Katz},
journal= {arXiv preprint arXiv:0803.0690},
year = {2009}
}
Comments
15 pages, 1 figure