Loewner's torus inequality with isosystolic defect

Charles Horowitz; Karin Usadi Katz; Mikhail G. Katz

doi:10.1007/s12220-009-9090-y

Loewner's torus inequality with isosystolic defect

Charles Horowitz, Karin Usadi Katz, Mikhail G. Katz

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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

Original language	English
Pages (from-to)	796-808
Number of pages	13
Journal	Journal of Geometric Analysis
Volume	19
Issue number	4
DOIs	https://doi.org/10.1007/s12220-009-9090-y
State	Published - 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).

Funding

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

Funders	Funder number
United States-Israel Binational Science Foundation	2006393
Israel Science Foundation	1294/06, 84/03

Keywords

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

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10.1007/s12220-009-9090-y

Cite this

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

keywords = "Bonnesen's inequality, Isosystolic defect, Loewner's torus inequality, Systole, Variance",

author = "Charles Horowitz and Katz, {Karin Usadi} and Katz, {Mikhail G.}",

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).",

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AU - Katz, Mikhail G.

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N2 - 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.

AB - 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.

KW - Bonnesen's inequality

KW - Isosystolic defect

KW - Loewner's torus inequality

KW - Systole

KW - Variance

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Loewner's torus inequality with isosystolic defect

Abstract

Bibliographical note

Funding

Keywords

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