Résume | Given a C2,α exterior domain Ω ⊂ Rn , n ≥ 3, we prove the existence of foliations of an open set in Ω x R by solutions to the exterior Dirichlet problem for the minimal surface equation in Ω with zero boundary data. We show that this foliation has horizontal ends and is parametrized by the maximal angle that the Gauss map of the leaves in Rn+1 make with the positive vertical axis at ∂Ω. Moreover, we show that any leaf has a limit height at infinity which can be estimated by the geometry of the domain.
Joint work with Jaime Ripoll (UFRGS/Brazil) and Daniel Bustos (Univ. del Tolima/Colombia). |