摘要
Let （M, g） be a complete Riemannian manifold of dimension d and Ricci curvaturebounded below by-K for some K∈. Let dx and p（x,y） be respectively the Riemannianvolum element and Riemannian distance. Consider L=△+V with V∈C<sup>2</sup>（M） satisfyingZ=∫<sub>m</sub>exp[V]dx 【 ∞. Then the L-diffusion process is reversible with respect to μ（dx）=Z<sup>-l</sup>exp[V]dx. It is well known that the exponentially L<sup>2</sup>-convergence of the L-diffusion pro-cess equivalent to a spectral gap
基金
Project partly supported by the National Natural Science Foundation of China and the State Education Commission of China.
