Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
Spectral Theory
2007-05-23 v3 Analysis of PDEs
Abstract
We give estimates for the norm () 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.
Cite
@article{arxiv.math/0506394,
title = {Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds},
author = {N. Burq and P. Gerard and N. Tzvetkov},
journal= {arXiv preprint arXiv:math/0506394},
year = {2007}
}
Comments
Completed the paper to include higher dimensional cases. In particular we now deal with general restriction of eigenfunctions on submanifolds