Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
复制标题
Laplace-Beltrami 特征函数对子流形的限制
DOI：
10.1215/s0012-7094-07-13834-1
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发表时间：
2005
影响因子：
2.5
通讯作者：
N. Tzvetkov
中科院分区：
文献类型：
--
作者：
N. Burq;P. Gérard;N. Tzvetkov
给出了黎曼曲面上Laplace Beltrami算子的本征函数曲线的约束的$L^p$范数($2leq p+inty$)的估计.如果曲线是测地线，我们证明在球面上这些估计是精确的。如果曲线具有非零测地曲率，我们可以改进我们的结果。我们还展示了我们的方法如何应用于高维流形。
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.