Regularity of area minimizing currents mod p

We establish a first general partial regularity theorem for area minimizing currents mod ( p ) , for every p , in any dimension and codimension. More precisely, we prove that the Hausdorff dimension of the interior singular set of an m -dimensional area minimizing current mod ( p ) cannot be larger...

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Bibliographic Details
Published inGeometric and functional analysis Vol. 30; no. 5; pp. 1224 - 1336
Main Authors De Lellis, Camillo, Hirsch, Jonas, Marchese, Andrea, Stuvard, Salvatore
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2020
Subjects
Analysis
Mathematics
Mathematics and Statistics
Area minimizing currents
Minimal surfaces
Center manifold
49N60
49Q05
49Q15
Regularity theory
35B65
Multiple valued functions
Blow-up analysis
35J47
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Summary:We establish a first general partial regularity theorem for area minimizing currents mod ( p ) , for every p , in any dimension and codimension. More precisely, we prove that the Hausdorff dimension of the interior singular set of an m -dimensional area minimizing current mod ( p ) cannot be larger than m - 1 . Additionally, we show that, when p is odd, the interior singular set is ( m - 1 ) -rectifiable with locally finite ( m - 1 ) -dimensional measure.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-020-00546-0