## Correspondences of hypersurfaces in hyperbolic Poincaré manifolds and conformally invariant PDEs

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- by Vincent Bonini, José M. Espinar and Jie Qing PDF
- Proc. Amer. Math. Soc.
**138**(2010), 4109-4117 Request permission

## Abstract:

On a hyperbolic Poincaré manifold, we derive an explicit relationship between the eigenvalues of Weyl-Schouten tensor of a conformal representative of the conformal infinity and the principal curvatures of the level sets of the associated geodesic defining function. This considerably simplifies the arguments and generalizes the results of Gálvez, Mira and the second author. In particular, we obtain the equivalence between Christoffel-type problems for hypersurfaces in a hyperbolic Poincaré manifold and scalar curvature problems on the conformal infinity.## References

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## Additional Information

**Vincent Bonini**- Affiliation: Department of Mathematics, California Polytechnic State University, San Luis Obispo, California 93407
- Email: vbonini@calpoly.edu
**José M. Espinar**- Affiliation: Departmento de Geometría y Topología, Universidad de Granada, E-18071 Granda, Spain
- Email: jespinar@ugr.es
**Jie Qing**- Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064
- MR Author ID: 268101
- Email: qing@ucsc.edu
- Received by editor(s): October 16, 2009
- Received by editor(s) in revised form: February 12, 2010
- Published electronically: June 11, 2010
- Communicated by: Matthew J. Gursky
- © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**138**(2010), 4109-4117 - MSC (2010): Primary 53C30, 53C40; Secondary 58J05
- DOI: https://doi.org/10.1090/S0002-9939-2010-10512-9
- MathSciNet review: 2679632