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Riemannian Manifolds With Uniformly Bounded Eigenfunctions by Toth, John; Zelditch, Steve is a scholarly article available to read on EtoBox.

What is Riemannian Manifolds With Uniformly Bounded Eigenfunctions about?

The standard eigenfunctions $\phi_{\lambda} = e^{i < \lambda, x >}$ on flat tori $\R^n / L$ have $L^{\infty}$-norms bounded independently of the eigenvalue. In the case of irrational flat tori, it follows that $L^2$-normalized eigenfunctions have uniformly bounded $L^{\infty}$-norms. Similar bases exist on other flat manifolds. Does this property characterize flat manifolds? We give an affirmative answer for compact Riemannian manifolds with completely integrable geodesic flows.

Author

Toth, John; Zelditch, Steve

Published

2000

Language

EN