Noether Symmetries of the Area-Minimizing Lagrangian

It is shown that the Lie algebra of Noether symmetries for the Lagrangian minimizing an n − 1 area enclosing a constant n-volume in a Euclidean space is so n ⊕sR and in a space of constant curvature the Lie algebra is so n . Furthermore, if the space has one section of constant curvature of dimension n1, another of n2, and so on to nk and one of zero curvature of dimension m, with n ≥ ∑kj 1 nj m as some of the sections may have no symmetry , then the Lie algebra of Noether symmetries is ⊕j 1so nj 1 ⊕ so m ⊕sR .