Le problème de Dirichlet pour des équations de Monge–Ampère complexes modifiées

Résumé 2m, g) be a strongly pseudoconvex hermitian manifold withC∞boundary. Ifϕbelongs toC2(X), let us consider the changes of hermitian metric defined byg1(ϕ)=−ϕg+i∂∂ϕandg±2(ϕ)=g+i∂∂ϕ±∇ϕ⊗∇ϕ. We solve problems of the form [detgi(ϕ)][det(g)]−1=F(x, ∇ϕ; ϕ) inXandϕ=uon ∂X, whereF∈C∞(TX×R) is an everywhere strictly positive function satisfying some assumptions andu∈C∞(∂X).