Some comparison results for one extension of the Bakry-Émery-Ricci tensor

2025/07/16 by Mota, Andrea M., Silva, Cristiano S., Miranda, Juliana F. R.
#Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2507.12594

Abstract

We consider generalizations of the drifted Laplacian and the Bakry-Émery-Ricci tensor, and we prove a version of the mean curvature comparison theorem. Consequently, we prove a Myers-type theorem and a generalization of the Cheeger-Gromoll splitting theorem.

Citations

• Two generalizations of Cheeger-Gromoll splitting theorem via Bakry-Émery Ricci curvature
• Comparison Geometry for the Bakry-Emery Ricci Tensor

Related

• Comparison Geometry for the Bakry-Emery Ricci Tensor
• Laplacian comparison theorem on Riemannian manifolds with modified m-Bakry-Emery Ricci lower bounds for m≤1
• Myers-type compactness theorem with the Bakry-Emery Ricci tensor
• Comparison geometry for an extension of Ricci tensor
• Comparison geometry for integral radial Bakry-Émery Ricci tensor bounds