Essential spectrum of the weighted Laplacian on noncompact manifolds and applications |
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Authors: | Adina Rocha |
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Institution: | 1.Instituto de Matemática,Universidade Federal de Alagoas,Maceió,Brazil |
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Abstract: | We obtain upper estimates for the bottom (that is, greatest lower bound) of the essential spectrum of weighted Laplacian operator of a noncompact 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. |
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