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Loewner’s Torus Inequality with Isosystolic Defect

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Abstract

We show that Bonnesen’s isoperimetric 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  \({\mathcal{G}}\) with respect to the flat metric of unit area in the conformal class of  \({\mathcal{G}}\) .

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Authors and Affiliations

  1. Department of Mathematics, Bar Ilan University, Ramat Gan, 52900, Israel

    Charles Horowitz, Karin Usadi Katz & Mikhail G. Katz

Authors
  1. Charles Horowitz
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  2. Karin Usadi Katz
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  3. Mikhail G. Katz
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Corresponding author

Correspondence to Charles Horowitz.

Additional information

M.G. Katz was supported by the Israel Science Foundation (grants no. 84/03 and 1294/06) and the BSF (grant 2006393).

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Horowitz, C., Katz, K.U. & Katz, M.G. Loewner’s Torus Inequality with Isosystolic Defect. J Geom Anal 19, 796–808 (2009). https://doi.org/10.1007/s12220-009-9090-y

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  • DOI: https://doi.org/10.1007/s12220-009-9090-y

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