Splitting theorems on complete manifolds with Bakry-Émery curvature

2011/12/29 by Wu, Jia-Yong
#53C24 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53C21 #Secondary 35P15

paper · doi:10.48550/arxiv.1112.6302

Abstract

In this paper we study some splitting properties on complete noncompact manifolds with smooth measures when ∞-dimensional Bakry-Émery Ricci curvature is bounded from below by some negative constant and spectrum of the weighted Laplacian has a positive lower bound. These results extend the cases of Ricci curvature and m-dimensional Bakry-Émery Ricci curvature.

Related

• The Splitting Theorem and Topology of Noncompact Spaces with Nonnegative\n N-Bakry 'Emery Ricci Curvature
• Bakry-Émery Ricci Curvature Bounds on Manifolds with Boundary
• A splitting theorem for manifolds with spectral nonnegative Ricci curvature and mean-convex boundary
• Spectral comparison and splitting theorems for the infinity-Bakry-Emery Ricci curvature
• A Spectral Splitting Theorem for the N-Bakry Émery Ricci tensor