Abstract
Let c:Λk−1→R+ be convex and Ω⊂Rn be a bounded domain. Let f0 and f1 be two closed k-forms on Ω satisfying appropriate boundary conditions. We discuss the minimization of ∫Ωc(A)dx over a subset of (k−1)-forms A on Ω such that dA+f1−f0=0, and its connection with a transport of symplectic forms. Section 3 mainly serves as a step toward Section 4, which is richer, as it connects to variational problems with multiple minimizers.
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