Quantum ergodic restriction theorems, II: manifolds without boundary

Details Quantum ergodic restriction theorems, II: manifolds without boundary Quantum ergodic restriction theorems, II: manifolds without boundary

2011-04-23

arxiv.org/abs/1104.4531v1

Mathematics

Spectral Theory

45 pages. Second in a series. The paper is self-contained; the methods and results are independent of the first article (arXiv

Scientific paper

We prove that if $(M, g)$ is a compact Riemannian manifold with ergodic geodesic flow, and if $H \subset M$ is a smooth hypersurface satisfying a generic microlocal asymmetry condition, then restrictions $\phi_j |_H$ of an orthonormal basis $\{\phi_j\}$ of $\Delta$-eigenfunctions of $(M, g)$ to $H$ are quantum ergodic on $H$. The condition on $H$ is satisfied by geodesic circles, closed horocycles and generic closed geodesics on a hyperbolic surface.

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