Estimates and monotonicity of the first eigenvalues under the Ricci flow on closed surfaces
Estimates and monotonicity of the first eigenvalues under the Ricci flow on closed surfaces
复制标题
闭合曲面上 Ricci 流下第一特征值的估计和单调性
DOI：
10.1007/s40304-015-0083-9
复制
发表时间：
2016
影响因子：
0.9
通讯作者：
Peng Zhu
中科院分区：
文献类型：
--
作者：
Shouwen Fang;Liang Zhao;Peng Zhu
In the paper we first derive the evolution equation for eigenvalues of geometric operatorunder the Ricci flow and the normalized Ricci flow on a closed Riemannian manifoldM, whereis the Witten–Laplacian operator,, andRis the scalar curvature. We then prove that the first eigenvalue of the geometric operator is nondecreasing along the Ricci flow on closed surfaces with certain curvature conditions when. As an application, we obtain some monotonicity formulae and estimates for the first eigenvalue on closed surfaces.
