Riemann流形上的加权Laplace算子

Weighted Laplacian operator on Riemannian manifolds

研究了 Riem ann流形上加权 L aplace算子 L 的第一特征值的下界估计问题 ,该问题是经典 L aplace算子的第一特征值估计的自然推广。鉴于应用数学的背景 ,法国数学家 Bakry在 1987年提出该问题。运用梯度估计中一些精巧的估计方法 ,推广了黎曼流形上加权 L aplace算子的结果 ,得到了 Riemann流形上加权 L

The estimate of the first eigenvalue of the weighted Laplacian operator on Riemannian manifolds is the natural generalization of the estimate of the first eigenvalue of the classical Laplacian operator. The French mathematician Bakry posed this problem in 1987 with a background of applied mathematics. This paper generalizes the known results to obtain sharp estimates of the first eigenvalue of the weighted Laplacian operator on Riemannian manifolds.