Corpus ID: 119590371

On the geometry of Riemannian manifolds with density

@article{Wylie2016OnTG,
  title={On the geometry of Riemannian manifolds with density},
  author={W. Wylie and Dmytro Yeroshkin},
  journal={arXiv: Differential Geometry},
  year={2016}
}

W. Wylie, Dmytro Yeroshkin

Published 2016

Mathematics

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… CONTINUE READING

View PDF on arXiv

Save to Library

Create Alert

Cite

Launch Research Feed