Phase transitions and minimal hypersurfaces in hyperbolic space.
Adriano Pisante,
(SAPIENZA, Università di Roma)
Miercoles 21 de abril 2010
Abstract: The purpose of this talk 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.