Title
Correspondences Of Hypersurfaces in Hyperbolic Poincaré Manifolds and Conformally Invariant PDEs
Recommended Citation
Published in Proceedings of the American Mathematical Society, Volume 138, Issue 11, November 1, 2010, pages 4109-4117.
The definitive version is available at https://doi.org/10.1090/S0002-9939-2010-10512-9.
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
Mathematics
Copyright
Publisher statement
This article was first published in Proceedings of the American Mathematical Society, published by the American Mathematical Society.
URL: https://digitalcommons.calpoly.edu/math_fac/47