Abstract
This paper proposes a direct approach to solve the Plateau's problem in codimension higher than one. The problem is formulated as the minimization of the Hausdorff measure among a family of d-rectifiable closed subsets of Rn: following the previous work [13], the existence result is obtained by a compactness principle valid under fairly general assumptions on the class of competitors. Such class is then specified to give meaning to boundary conditions. We also show that the obtained minimizers are regular up to a set of dimension less than (d-1).
| Original language | English (US) |
|---|---|
| Pages (from-to) | 59-80 |
| Number of pages | 22 |
| Journal | Advances in Mathematics |
| Volume | 288 |
| DOIs | |
| State | Published - Jan 22 2016 |
Keywords
- Geometric measure theory
- Plateau's problem
- Rectifiable sets
ASJC Scopus subject areas
- Mathematics(all)
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Cite this
De Philippis, G., De Rosa, A., & Ghiraldin, F. (2016). A direct approach to Plateau's problem in any codimension. Advances in Mathematics, 288, 59-80. https://doi.org/10.1016/j.aim.2015.10.007