Loewner's torus inequality with isosystolic defect

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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

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Differential Geometry, Analysis of PDEs, Complex Variables, Metric Geometry, 53C23 (Primary); 30F10, 35J60, 58J60 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/219360

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0803.0690
 http://arxiv.org/abs/0803.0690

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arXiv