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

Hebda, James

doi:10.1090/tran/7794

The primitive length spectrum of 2-D tori and generalized Loewner inequalities
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Trans. Amer. Math. Soc. 372 (2019), 6371-6401 Request permission

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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