The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension

Complex Ginzburg-landau Equations in High Dimensions and Codimension Two Area Minimizing Currents. Part I: the Dimension Three Case

Singular Levi-flat Hypersurfaces and Codimension One Foliations

We study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular

Complex Ginzburg-landau Equations in High Dimensions and Codimension Two Area Minimizing Currents. Part Ii : a Proof of the Eta-compactness in Dimension N > 3

Regularity of Area Minimizing Currents Iii: Blow-up

This is the last of a series of three papers in which we give a new, shorter proof of a slightly improved version of Almgren’s partial regularity of area minimizing currents in Riemannian manifolds. Here we perform a blow-up analysis deducing the regularity of area minimizing currents from that of Dir-minimizing multiple valued functions. 0. Introduction In this paper we complete the proof of a...

Regularity of Area Minimizing Currents I: Gradient L Estimates

In a series of papers, including the present one, we give a new, shorter proof of Almgren’s partial regularity theorem for area minimizing currents in a Riemannian manifold, with a slight improvement on the regularity assumption for the latter. This note establishes a new a priori estimate on the excess measure of an area minimizing current, together with several statements concerning approxima...