Manifolds with Density and Perelman's Proof of the Poincaré Conjecture

@article{Morgan2009ManifoldsWD,
  title={Manifolds with Density and Perelman's Proof of the Poincar{\'e} Conjecture},
  author={Frank Morgan},
  journal={The American Mathematical Monthly},
  year={2009},
  volume={116},
  pages={134 - 142},
  url={https://api.semanticscholar.org/CorpusID:6068179}
}
1. DEFINITIONS. A manifold with density is a Riemannian manifold Mn (n dimensional surface with an infinitesimal arclength ds that you can use to compute lengths, areas, and volumes) with a positive
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