In this note we revisit Almgren's theory of Q-valued functions, that are functions taking values in the space of unordered Q-tuples of points in Rn. In particular: we give shorter versions of Almgren's proofs of the existence of Dir-minimizing Q-valued functions, of their Hölder regularity and of the dimension estimate of their singular set.
Q-valued functions revisited / DE LELLIS, Camillo; Spadaro, EMANUELE NUNZIO. - In: MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0065-9266. - 211:991(2011), pp. 1-85. [10.1090/S0065-9266-10-00607-1]
Q-valued functions revisited
Camillo De Lellis;Emanuele Spadaro
2011
Abstract
In this note we revisit Almgren's theory of Q-valued functions, that are functions taking values in the space of unordered Q-tuples of points in Rn. In particular: we give shorter versions of Almgren's proofs of the existence of Dir-minimizing Q-valued functions, of their Hölder regularity and of the dimension estimate of their singular set.File allegati a questo prodotto
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