In this talk, we will talk about how to get a sharp lower bound estimate for the first nonzero eigenvalue of the sub-Laplacian, Kohn Laplacian, and Folland- Stein operator, on a closed strictly pseudoconvex CR (2n+1)-manifold. We also discuss the case when a sharp lower bound estimate of the sub-Laplacian or Kohn Laplacian is achieved. It can be showed that such a manifold is the standard CR (2n+1)-sphere.
