In this paper we obtain lower bounds for the first eigenvalue to some kinds of the eigenvalue problems for Bi-drifted Laplacian operator on compact manifolds (also called a smooth metric measure space) with boundary and m-Bakry-Emery Ricci curvature or Bakry-Emery Ricci curvature bounded below. We also address the eigenvalue problem with Wentzell-type boundary condition for drifted Laplacian on smooth metric measure space.

中文翻译：

---

平滑度量空间上双向漂移拉普拉斯算子的第一特征值的估计

在本文中，我们获得了具有边界和m -Bakry-Emery Ricci 曲率或 Bakry-Emery 的紧凑流形（也称为平滑度量空间）上的双向漂移拉普拉斯算子的某些特征值问题的第一特征值的下界Ricci 曲率限制在下方。我们还解决了平滑度量空间上漂移拉普拉斯算子的 Wentzell 型边界条件的特征值问题。