Differential Geometry Seminar: Eigenvalue estimates and differential form Laplacians on Alexandrov spaces
Seminar | February 12 | 2:10-3 p.m. | 939 Evans Hall
John Lott, UC Berkeley
In S.-Y. Cheng's Berkeley thesis from 1974, he gave upper bounds on the eigenvalues of the function Laplacian on a compact Riemannian manifold, in terms of geometric data. I will give an extension of Cheng's results to the differential form Laplacian. The proof uses Alexandrov spaces, i.e. metric spaces with curvature bounded below. I will also construct differential form Laplacians on Alexandrov spaces and prove a Hodge theorem.