Calculus of Variations and Geometric Measure Theory

L. Ambrosio - C. De Lellis - T. Schmidt

Partial regularity for mass-minimizing currents in Hilbert spaces

created by schmidt on 06 Mar 2013
modified on 01 Mar 2018


Published Paper

Inserted: 6 mar 2013
Last Updated: 1 mar 2018

Journal: J. Reine Angew. Math.
Volume: 734
Pages: 99-144
Year: 2018
Links: Link to the published version


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.

Tags: GeMeThNES