Essential Spectrum of the Weighted Laplacian on Noncompact Manifolds and Applications
arXiv:1608.01539 · doi:10.1007/s10711-016-0186-9
Abstract
We obtain upper estimates for the bottom (that is, greatest lower bound) of the essential spectrum of weighted Laplacian operator of a weighted manifold under assumptions of the volume growth of their geodesic balls and spheres. Furthermore, we find examples where the equality occurs in the estimates obtained. As a consequence, we give estimates for the weighted mean curvature of complete noncompact hypersurfaces into weighted manifolds.