查询词典 laplace beltrami operator

In this thesis, we mainly study several problems on geometry and topology of Rieman-nian submanifolds, which contains the geometric rigidity, topological sphere theorems and eigenvalue problems of Laplace-Beltrami operator on Riemannian submanifolds.

本文着重研究黎曼子流形上几何与拓扑的若干问题，主要内容包括子流形的几何刚性、拓扑球面定理和Laplace-Beltrami算子的特征值问题。

For the case of waveduide R~2×M, where M be Zoll manifolds, if the initial data is small enough, we can use the special distribution of eigenvalues of Laplace-Beltrami operator on Zoll manifold, the estimate of the energy and the technique of normal form to prove the existence of global solutions for nonlinear Klein-Gordon equations.

对波管R~2×M上的非线性Klein-Gordon方程，其中M为Zoll流形，如果初值足够小，利用Zoll流形上Laplace-Beltrami算子的特征值的分布，并结合能量估计和法形式技巧，我们证明了整体解的存在性。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。