Eigenvalues under the Ricci flow of model geometries

Abstract

In this paper, we study the evolving behaviors of the first eigenvalue of Laplace-Beltrami operator under the normalized Ricci flow of model geometries. In every Bianchi class, we estimate the derivative of the eigenvalue. Then we construct monotonic quantities under the Ricci flow and obtain upper and lower bounds for the eigenvalue.

15 pages

References in corpus (3)

• A Class of Monotonic Quantities along the Ricci Flow
• Some Asymptotic Behavior of the first Eigenvalue along the Ricci Flow
• Eigenvalues under the backward Ricci flow on locally homogeneous closed 3-manifolds