Partial regularity of almost minimizing rectifiable G chains in Hilbert space

Abstract

We adapt to an infinite dimensional ambient space E.R. Reifenberg's epiperimetric inequality and a quantitative version of D. Preiss' second moments computations to establish that the set of regular points of an almost mass minimizing rectifiable $G$ chain in ${\ell }_2$ is dense in its support, whenever the group $G$ of coefficients is so that $\{\Vert g\Vert :g\in G\}$ is discrete and closed.

arXiv comment96 pages