Weighted Laplacian operator on Riemannian manifolds
Huixia He · Journal of Tsinghua University(Science and Technology) · 2004
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.