In this paper, two interesting eigenvalue comparison theorems for the first non-zero Steklov eigenvalue of the Laplacian have been established for manifolds with radial sectional curvature bounded from above. Besides, sharper bounds for the first non-zero eigenvalue of the Wentzell eigenvalue problem of the weighted Laplacian, which can be seen as a natural generalization of the classical Steklov eigenvalue problem, have been obtained.

中文翻译：

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Steklov特征值问题中的特征值比较和其他一些特征值估计

本文针对径向截面曲率从上限定边界的流形，建立了拉普拉斯算子的第一个非零Steklov特征值的两个有趣的特征值比较定理。此外，已获得加权拉普拉斯算子的Wentzell特征值问题的第一个非零特征值的更清晰的边界，这可以看作是经典Steklov特征值问题的自然概括。