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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Wu, JY. A note on the splitting theorem for the weighted measure. Ann Glob Anal Geom 43, 287–298 (2013). https://doi.org/10.1007/s10455-012-9346-9
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DOI: https://doi.org/10.1007/s10455-012-9346-9