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Essential Spectrum of the Weighted Laplacian on Noncompact Manifolds and Applications (1608.01539v1)
Published 4 Aug 2016 in math.DG
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.