Author:
De Lellis Camillo,Hirsch Jonas,Marchese Andrea,Stuvard Salvatore
Abstract
AbstractWe establish a first general partial regularity theorem for area minimizing currents$${\mathrm{mod}}(p)$$mod(p), for everyp, in any dimension and codimension. More precisely, we prove that the Hausdorff dimension of the interior singular set of anm-dimensional area minimizing current$${\mathrm{mod}}(p)$$mod(p)cannot be larger than$$m-1$$m-1. Additionally, we show that, whenpis odd, the interior singular set is$$(m-1)$$(m-1)-rectifiable with locally finite$$(m-1)$$(m-1)-dimensional measure.
Funder
Università degli Studi di Trento
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Analysis
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