Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold
Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold
复制标题
闭黎曼流形上拉普拉斯算子本征函数的集中
DOI：
10.1090/proc/14430
复制
发表时间：
2019
影响因子：
1
通讯作者：
Kei Funano and Yohei Sakurai
中科院分区：
文献类型：
--
作者：
Kei Funano and Yohei Sakurai
研究了闭黎曼流形上拉普拉斯本征函数的集中现象。证明了闭流形的体积测度以指数形式集中在特征函数的节点集周围。利用Colding和Minicozzi的方法，证明了本征函数的受限指数浓度不等式和受限sogge型估计。参考文献
We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponentially. Applying the method of Colding and Minicozzi we also prove restricted exponential concentration inequalities and restricted Sogge-typemoment estimates of eigenfunctions. References