论文标题
Kato型RICCI曲率条件的特征值估计值
Eigenvalue estimates for Kato-type Ricci curvature conditions
论文作者
论文摘要
我们证明，最佳的下部特征值估计值对钟阳的类型以及第一个特征值的钟型上限，在闭合歧管上保留，假设Ricci曲率的负部分只有Kato条件。这将所有较早的结果概括为$ l^p $ - 外观假设。此外，我们在诺伊曼·拉普拉斯（Neumann Laplacian）方面引入了带边界的紧凑型歧管的加藤条件，从而导致Harnack估计Neumann Heat内核，并为所有Neumann特征值的下界和下限，这为这种情况下的所有Neumann特征值提供了最初的见解。
We prove that optimal lower eigenvalue estimates of Zhong-Yang type as well as a Cheng-type upper bound for the first eigenvalue hold on closed manifolds assuming only a Kato condition on the negative part of the Ricci curvature. This generalizes all earlier results on $L^p$-curvature assumptions. Moreover, we introduce the Kato condition on compact manifolds with boundary with respect to the Neumann Laplacian, leading to Harnack estimates for the Neumann heat kernel and lower bounds for all Neumann eigenvalues, what provides a first insight in handling variable Ricci curvature assumptions in this case.
