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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The eigenvalue spectrum as moduli for flat tori


Author: Scott Wolpert
Journal: Trans. Amer. Math. Soc. 244 (1978), 313-321
MSC: Primary 53C99; Secondary 58G99
MathSciNet review: 0514879
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0514879-9
PII: S 0002-9947(1978)0514879-9
Keywords: Flat torus, Laplace Beltrami operator, spectrum, moduli, lattice, quadratic forms
Article copyright: © Copyright 1978 American Mathematical Society