The eigenvalue spectrum as moduli for flat tori

Wolpert, Scott

doi:10.1090/S0002-9947-1978-0514879-9

The eigenvalue spectrum as moduli for flat tori
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Trans. Amer. Math. Soc. 244 (1978), 313-321 Request permission

Abstract:

A flat torus T carries a natural Laplace Beltrami operator. It is a conjecture that the spectrum of the Laplace Beltrami operator determines T modulo isometries. We prove that, with the exception of a subvariety in the moduli space of flat tori, this conjecture is true. A description of the subvariety is given.

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