Existence of Minimizers for the Reifenberg Plateau problem

الأصل · EN

That is, given a compact set B ⊂ Rⁿ (the boundary) and a subgroup L of the Čech homology group Hd₋₁(B;G) of dimension d over some commutative group G, we find a compact set E ⊃ B such that the image of L by the natural map Hd₋₁(B;G)→Hd₋₁(S;G) induced by the inclusion B → E, is reduced to { 0 }, and such that the Hausdorff measure Hᵈ(E B) is minimal under these constraints. Thus we have no restriction on the group G or the dimensions 0 < d < n.