L Concentration Estimates for the Laplacian Eigenfunctions near Submanifolds
نویسنده
چکیده
We study L bounds on spectral projections for the Laplace operator on compact Riemannian manifolds, restricted to small frequency dependent neighborhoods of submanifolds. In particular, if λ is a frequency and the size of the neigborhood is O(λ−δ), then new sharp estimates are established when δ ≥ 1, while for 0 ≤ δ ≤ 1/2, Sogge’s estimates [17] turn out to be optimal. In the intermediate region 1/2 < δ < 1, we sometimes get sharp estimates as well. Our arguments follow closely the recent work [7] by Burq and Zuily.
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