A note on the splitting theorem for the weighted measure |
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Authors: | Jia-Yong Wu |
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Institution: | 1. Department of Mathematics, Shanghai Maritime University, Haigang Avenue 1550, Shanghai, 201306, People’s Republic of China
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Abstract: | In this paper, we study complete manifolds equipped with smooth measures whose spectrum of the weighted Laplacian has an optimal positive lower bound and the m-dimensional Bakry–Émery Ricci curvature is bounded from below by some negative constant. In particular, we prove a splitting type theorem for complete smooth measure manifolds that have a finite-weighted volume end. This result is regarded as a study of the equality case of an author’s theorem (Wu, J Math Anal Appl 361:10–18, 2010). |
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