A “quasi maximum principle” for I-surfaces

The result of this paper yields a maximum principle for the components of surfaces whose distortion by a certain GL3(R) matrix are minimizers of a dominance functional I of a parametric functional J with dominant area term within boundary value classes , termed I-surfaces. Finally we derive a compactness result for sequences of I-surfaces in , which serves as a preparation for the forthcoming article [R. Jakob, Unstable extremal surfaces of the “Shiffman functional” spanning rectifiable boundary curves, Calc. Var., submitted for publication] whose aim is a proof of a sufficient condition for the existence of extremal surfaces of J which do not furnish global minima of J within the class C∗(Γ) of H1,2-surfaces spanning an arbitrary closed rectifiable boundary curve Γ⊂R3 that merely has to satisfy a chord-arc condition.