关于极小嵌入超曲面第一特征值的一个注记

A Note on the First Eigenvalue for Embedded Minimal Hypersurfaces

设N是Ricci曲率以正常数k为下界的n+1维紧致定向黎曼流形,M是嵌入在N中的定向极小闭超曲面.本文给出M上Laplace算子的第一特征值λ1的新的下界估计,改进了已有结论,使之更接近于丘成桐关于该问题的猜想.

Let M be a compact orientable minimal hypersurface embedded in a compact orientable Riemannian manifold N with Ricci curvature bounded from below by a positive constant k.A new lower bound of λ1,the first closed eigenvalue of the Laplacian on M was given.The result improved the related ones and could be regarded as some evidence that Yau＇s conjecture may be true.