A note on the splitting theorem for the weighted measure
Differential Geometry
2012-08-23 v3
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 -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).
Cite
@article{arxiv.1112.0732,
title = {A note on the splitting theorem for the weighted measure},
author = {Jia-Yong Wu},
journal= {arXiv preprint arXiv:1112.0732},
year = {2012}
}
Comments
11 pages, minor typos corrected