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Let  G  be a finite group of isometries acting on a complete Riemannian manifold. Suppose that  B  is a 0-dimensional boundary which is  G -invariant. If the order of  G  divides the product of the cardinality of the orbit and the density of  B  at each point, then a  G -invariant absolutely length minimizing integral current with boundary  B  can be constructed.

Finite groups and invariant solutions to one-dimensional Plateau problems