Loewner's torus inequality with isosystolic defect

Charles Horowitz, Karin Usadi Katz, Mikhail G. Katz

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 G with respect to the flat metric of unit area in the conformal class of G.

Original languageEnglish
Pages (from-to)796-808
Number of pages13
JournalJournal of Geometric Analysis
Issue number4
StatePublished - Oct 2009

Bibliographical note

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


  • Bonnesen's inequality
  • Isosystolic defect
  • Loewner's torus inequality
  • Systole
  • Variance


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