The standard eigenfunctions ϕλ = ei⟨λ, x⟩ on flat tori ℝn/L have L∞-norms bounded independently of the eigenvalue. In the case of irrational flat tori, it follows that L∞-normalized eigenfunctions have uniformly bounded L1-norms. Similar bases exist on other flat manifolds. Does this property characterize flat manifolds? We give an affirmative answer for compact Riemannian manifolds with quantum completely integrable Laplacians.
|Original language||English (US)|
|Number of pages||36|
|Journal||Duke Mathematical Journal|
|State||Published - 2002|
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