A note on the splitting theorem for the weighted measure

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

11 pages, minor typos corrected

References in corpus (1)

• Splitting theorems on complete manifolds with Bakry-Émery curvature

Cited by in corpus (4)

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