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Partial regularity of almost minimizing rectifiable G chains in Hilbert space
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 141, Number 6, December 2019
- pp. 1591-1705
- 10.1353/ajm.2019.0044
- Article
- Additional Information
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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 $\{\|g\|:g\in G\}$ is discrete.