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arXiv · 1608.01539

Essential Spectrum of the Weighted Laplacian on Noncompact Manifolds and Applications

Adina Rocha
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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 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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Adina Rocha. 2016-08-04. Essential Spectrum of the Weighted Laplacian on Noncompact Manifolds and Applications. https://doi.org/10.1007/s10711-016-0186-9

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