O problema de Dirichlet para a equação das hipersuperfícies mínimas em domínios arbitrários de uma variedade Riemanniana

Abstract

In this work we study the Dirichlet problem for the minimal graph equation on C2-domains Ω ⊂ M , where M is an arbitrary complete Riemanniam manifold. We show that, in the case where Ω is bounded, for ϕ ∈ C2(∂Ω), there exists a constant C = C(|Dϕ|, |D2ϕ|, |II|, RicM ), where |II| is the norm of the second fundamental form of ∂Ω, for which the Dirichlet pro- blem has a solution since osc(ϕ) ≤ C.