Laplacian第一特征值整体曲率Pinching的一个结果

A Global Curvature Pinching Result of the First Eigenvalue of Laplacian

紧致流形上Laplacian的第一特征值的下界估计一直以来是人们非常感兴趣的问题之一.本文在整体曲率Pinching较小的条件之下考虑这个问题,得到了相应几何条件之下的Laplacian第一特征值的一个下界估计.

The lower bound of the first eigenvalue of Laplacian on closed manifolds is always a very interesting problem. We study this subject in this paper under the assumption of small global curvature pinching. Finally, we derive a lower bound of the first eigenvalue of Laplacian according to the geometry of the manifolds.