Eigenvalue estimate for the rough Laplacian on differential forms - Colbois, Bruno; Maerten, Daniel (My University, 2010)
We study the spectrum of the rough Laplacian acting on differential forms on a compact Riemannian manifold (M,g). We first construct on M metrics of volume 1 whose spectrum is as large as desired. Then, provided that the Ricci curvature of g is bounded below, we relate the spectrum of the rough Laplacian on 1--forms to the spectrum of the Laplacian on functions, and derive some upper bound in agreement with the asymptotic Weyl law.
Keywords: Rough Laplacian; eigenvalue estimate; differential forms; Weyl law