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Quantum limits on flat tori. (English) Zbl 0874.58088
The author classifies all weak$$^*$$ limits of squares of normalized eigenfunctions of the Laplacian on two-dimensional flat tori (the so-called quantum limits). He also obtains several results on such limits in dimensions 3 and higher.

##### MSC:
 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 58C40 Spectral theory; eigenvalue problems on manifolds 52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)
##### Keywords:
Laplacian; flat tori; quantum limits
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