A splitting theorem for the weighted measure |
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Authors: | Lin Feng Wang |
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Institution: | 1. School of Science, Nantong University, Nantong, 226007, Jiangsu, China
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Abstract: | Let M be an n-dimensional complete noncompact Riemannian manifold, h be a smooth function on M and dμ = e
h
dV be the weighted measure. In this article, we prove that when the spectrum of the weighted Laplacian
\trianglem{\triangle_{\mu}} has a positive lower bound λ1(M) > 0 and the m(m > n)-dimensional Bakry-émery curvature is bounded from below by
-\fracm-1m-2l1(M){-\frac{m-1}{m-2}\lambda_1(M)}, then M splits isometrically as R × N whenever it has two ends with infinite weighted volume, here N is an (n − 1)-dimensional compact manifold. |
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Keywords: | |
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