Quantum limits on flat tori. (English) Zbl 0874.58088

Jakobson, Dmitry

Ann. Math. (2) 145, No. 2, 235-266 (1997).

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.

Reviewer: M.Puta (Timişoara)

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