• Corpus ID: 119590371

On the geometry of Riemannian manifolds with density

  title={On the geometry of Riemannian manifolds with density},
  author={William C. Wylie and Dmytro Yeroshkin},
  journal={arXiv: Differential Geometry},
We introduce a new geometric approach to a manifold equipped with a smooth density function that takes a torsion-free affine connection, as opposed to a weighted measure or Laplacian, as the fundamental object of study. The connection motivates new versions of the volume and Laplacian comparison theorems that are valid for the 1-Bakry-Emery Ricci tensor, a weaker assumption than has previously been considered in the literature. As applications we prove new generalizations of Myers' theorem and… 

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