Eigenvalues of the Laplacian on a compact manifold with density
Eigenvalues of the Laplacian on a compact manifold with density
In this paper, we study the spectrum of the weighted Laplacian (also called Bakry-Emery or Witten Laplacian) Lσ on a compact, connected, smooth Riemannian manifold (M, g) endowed with a measure σdvg.First, we obtain upper bounds for the k-th eigenvalue of Lσ which are consistent with the power of k …