Ricci curvature in the neighborhood of rank-one symmetric spaces

@article{Delay2001RicciCI,
  title={Ricci curvature in the neighborhood of rank-one symmetric spaces},
  author={Erwann Delay and Marc Herzlich},
  journal={The Journal of Geometric Analysis},
  year={2001},
  volume={11},
  pages={573-588}
}
We study the Ricci curvature of a Riemannian metric as a differential operator acting on the space of metrics close (in a weighted functional spaces topology) to the standard metric of a rank-one noncompact symmetric space. We prove that any symmetric bilinear field close enough to the standard may be realized as the Ricci curvature of a unique close metric if its decay rate at infinity (its weight) belongs to some precisely known interval. We also study what happens if the decay rate is too… 

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