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Lower bounds for the first eigenvalue of the Laplacian on Kähler manifolds
Transactions of the American Mathematical Society ( IF 1.2 ) Pub Date : 2021-08-30 , DOI: 10.1090/tran/8434
Xiaolong Li , Kui Wang

Abstract:We establish lower bound for the first nonzero eigenvalue of the Laplacian on a closed Kähler manifold in terms of dimension, diameter, and lower bounds of holomorphic sectional curvature and orthogonal Ricci curvature. On compact Kähler manifolds with boundary, we prove lower bounds for the first nonzero Neumann or Dirichlet eigenvalue in terms of geometric data. Our results are Kähler analogues of well-known results for Riemannian manifolds.


中文翻译:

Kähler 流形上拉普拉斯算子的第一特征值的下界

摘要:我们根据尺寸、直径以及全纯截面曲率和正交 Ricci 曲率的下界,为封闭的 Kähler 流形上的拉普拉斯算子的第一个非零特征值建立了下界。在具有边界的紧凑 Kähler 流形上,我们证明了第一个非零 Neumann 或 Dirichlet 特征值的几何数据下界。我们的结果是黎曼流形的著名结果的 Kähler 类似物。
更新日期:2021-10-21
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