Q-valued Functions Revisited
نویسندگان
چکیده
Abstract. In this note we revisit Almgren’s theory of Q-valued functions, that are functions taking values in the space AQ(R) of unorderedQ-tuples of points in R. In particular: • we give shorter versions of Almgren’s proofs of the existence of Dir-minimizing Qvalued functions, of their Hölder regularity and of the dimension estimate of their singular set; • we propose an alternative intrinsic approach to these results, not relying on Almgren’s biLipschitz embedding ξ : AQ(R) → R; • we improve upon the estimate of the singular set of planar Dir-minimizing functions by showing that it consists of isolated points.
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