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Transactions of the American Mathematical Society

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The primitive length spectrum of 2-D tori and generalized Loewner inequalities


Author: James J. Hebda
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 53C20; Secondary 53C22
DOI: https://doi.org/10.1090/tran/7794
Published electronically: March 15, 2019
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Abstract: We develop inequalities between the primitive length spectrum and area of a Riemannian metric on a two-dimensional torus. These inequalities may be regarded as generalizations of Loewner's famous inequality. They also lead to generalizations of higher-dimensional systolic inequalities when the Betti numbers are $ 2$.


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Additional Information

James J. Hebda
Affiliation: Department of Mathematics and Computer Science, Saint Louis University, St. Louis, Missouri 63103
Email: hebdajj@slu.edu

DOI: https://doi.org/10.1090/tran/7794
Received by editor(s): December 22, 2015
Received by editor(s) in revised form: December 20, 2018
Published electronically: March 15, 2019
Article copyright: © Copyright 2019 American Mathematical Society