%0 Journal Article
%T A note on the splitting theorem for the weighted measure
%A Jia-Yong Wu
%J Mathematics
%D 2011
%I arXiv
%R 10.1007/s10455-012-9346-9
%X 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).
%U http://arxiv.org/abs/1112.0732v3