The Singular Set of 1-1 Integral Currents

2003/10/04 by Tristan Riviere, Gang Tian, Riviere, Tristan +1 · 2 citations
Mathematics · #32Q65 #49Q05 #49Q15 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:32Q65 #msc:49Q05 #msc:49Q15

paper · pdf · doi:10.48550/arxiv.math/0310052

67 pages

arxiv created 2003/10/04 · arxiv updated 2009/12/01

Abstract

We prove that 2 dimensional Integral currents (i.e. integer multiplicity 2 dimensional rectifiable currents) which are almost complex cycles in an almost complex manifold admitting locally a compatible symplectic form are smooth surfaces aside from isolated points and therefore are J-holomorphic curves.

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• Minimizing the Gauss map area of surfaces in \mathbbS³
• Symmetric log-epiperimetric inequality for harmonic maps with analytic target and applications

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