Published Paper
Inserted: 6 mar 2013
Last Updated: 1 mar 2018
Journal: J. Reine Angew. Math.
Volume: 734
Pages: 99-144
Year: 2018
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Link to the published version
Abstract:
Recently, the theory of currents and the existence theory for Plateau's problem have been extended to the case of finite-dimensional currents in infinite-dimensional manifolds or even metric spaces; see [5] (and also [7,37] for the most recent developments). In this paper, in the case when the ambient space is Hilbert, we provide the first partial regularity result, in a dense open set of the support, for $n$-dimensional integral currents which locally minimize the mass. Our proof follows with minor variants [32], implementing Lipschitz approximation and harmonic approximation without indirect arguments and with estimates which depend only on the dimension $n$ and not on codimension or dimension of the target space.
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