Convergence of solutions of H-systems or how to blow bubbles

Soit Γ⊂R 3 une courbe de Jordan. On cherche des surfaces de courbure moyenne constante delimitees par Γ. On considere des surfaces Σ parametrisees sur le disque unite: Ω={(x,y)∈R 2 ; x 2 +y 2 <1} et Σ=u(Ω), ou u:Ω→R 3 satisfait Δu=2u x u y sur Ω, |u x | 2 −|u y | 2 =u x •u y =0 sur Ω, u(∂Ω)=Γ. On etudie le comportement de telles surfaces quand Γ→0

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