We establish a theory of Q-valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently area minimizing currents mod(p) when p=2Q, and to establish a first general partial regularity theorem for every p in any dimension and codimension.
Area minimizing currents mod $2Q$: linear regularity theory / C. De Lellis, J. Hirsch, A. Marchese, S. Stuvard. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 75:1(2022 Jan), pp. 83-127. [10.1002/cpa.21964]
Area minimizing currents mod $2Q$: linear regularity theory
S. Stuvard
2022
Abstract
We establish a theory of Q-valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently area minimizing currents mod(p) when p=2Q, and to establish a first general partial regularity theorem for every p in any dimension and codimension.
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