Correspondences Of Hypersurfaces in Hyperbolic Poincaré Manifolds and Conformally Invariant PDEs
Proceedings of the American Mathematical Society
  • Vincent Bonini , California Polytechnic State University - San Luis Obispo
  • José M. Espinar , Universidad de Granada
  • Jie Qing , University of California - Santa Cruz
Article
Publication Date
11-1-2010
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 Poincar´e manifold and scalar curvature problems on the conformal infinity.
Disciplines
Citation Information
Vincent Bonini, José M. Espinar and Jie Qing. "Correspondences Of Hypersurfaces in Hyperbolic Poincaré Manifolds and Conformally Invariant PDEs" Proceedings of the American Mathematical Society Vol. 138 Iss. 11 p. 4109 - 4117
Available at: http://works.bepress.com/vbonini/3/
Publisher statement
This article was first published in Proceedings of the American Mathematical Society, published by the American Mathematical Society.