论文标题
Neumann和Steklov特征值的谐波平均值的共形和外部上限
Conformal and extrinsic upper bounds for the harmonic mean of Neumann and Steklov eigenvalues
论文作者
论文摘要
令$ m $为$ m $二维紧凑型riemannian带有边界的歧管。我们获得了第一个$ m $ nozero neumann特征值和Steklov特征值的谐波平均值的上限，分别涉及共形体积和相对保形体积。我们还为空间形式的封闭子延伸物提供了最佳的尖锐外部上限。这些扩展了第一个非零特征值的先前相关结果。
Let $M$ be an $m$-dimensional compact Riemannian manifold with boundary. We obtain the upper bound of the harmonic mean of the first $m$ nonzero Neumann eigenvalues and Steklov eigenvalues involving the conformal volume and relative conformal volume, respectively. We also give an optimal sharp extrinsic upper bound for closed submanifolds in the space forms. These extend the previous related results for the first nonzero eigenvalue.
