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.

Regularity of area minimizing currents mod p / C. De Lellis, J. Hirsch, A. Marchese, S. Stuvard. - In: GEOMETRIC AND FUNCTIONAL ANALYSIS. - ISSN 1016-443X. - 30:5(2020 Oct 30), pp. 1224-1336.

Regularity of area minimizing currents mod p

S. Stuvard
2020-10-30

Abstract

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.
area minimizing currents mod p; regularity theory; minimal surfaces; multiple valued functions; blow-up analysis
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/850248
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