A note on the splitting theorem for the weighted measure

Details A note on the splitting theorem for the weighted measure A note on the splitting theorem for the weighted measure

2011-12-04

arxiv.org/abs/1112.0732v3

Mathematics

Differential Geometry

11 pages, minor typos corrected

Scientific paper

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-\'Emery 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 (J. Math. Anal. Appl. 361 (2010) 10-18).

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