Inserted: 8 feb 2010
The purpose of this paper is to investigate the Cahn-Hillard approximation for entire minimal hypersurfaces in the hyperbolic space. Combining comparison principles with minimization and blow-up arguments, we prove existence results for entire local minimizers with prescribed behaviour at infinity. Then, we study the limit as the length scale tends to zero through a Gamma-convergence analysis, obtaining existence of entire minimal hypersurfaces with prescribed boundary at infinity. In particular, we recover some existence results proved by M. Anderson and U. Lang using geometric measure theory.
Keywords: phase transitions, Hyperbolic space, boundary value problems, minimal hypersurfaces