Mathematics – Spectral Theory
Scientific paper
2005-06-20
Mathematics
Spectral Theory
Completed the paper to include higher dimensional cases. In particular we now deal with general restriction of eigenfunctions
Scientific paper
We give estimates for the $L^p$ norm ($2\leq p \leq +\infty$) of the restriction to a curve of the eigenfunctions of the Laplace Beltrami operator on a Riemannian surface. If the curve is a geodesic, we show that on the sphere these estimates are sharp. If the curve has non vanishing geodesic curvature, we can improve our results. We also show how our approach apply to higher dimensional manifolds.
Burq Nicolas
Gérard Patrick
Tzvetkov Nikolay
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