Dissertação
O problema de Dirichlet para a equação das hipersuperfícies mínimas em domínios arbitrários de uma variedade Riemanniana
Autor
Priebe, Lucas Soares
Institución
Resumen
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.