在本篇文章中，我們研究有非負巴克里-埃默瑞里奇曲率的完備光滑賦距測度空間上加權拉普拉斯算子的函數定理及頻譜性質。主要的結果包含加權拉普拉斯算子的最低頻譜上界、光滑賦距測度空間的分裂定理、正加權調和函數的梯度估計以及多項式增長加權調和函數空間的維度估計。

In this paper, we study some function theorems and spectrum properties of f-Laplacian on a complete smooth metric measure space (M, g, e^{-f} dv) with nonnegative Bakry-Émery Ricci curvature. The main results include the upper bound of the bottom spectrum of the f-Laplacian, the splitting theorem of the smooth metric measure space, a gradient estimate for positive f-harmonic function and dimension estimate of the space of polynomial growth f-harmonic functions.

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