The singular set of 1-1 integral currents


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


Tristan Rivière

Department of Mathematics
ETH Zentrum
8092 Zürich

Gang Tian

Department of Mathematics
Princeton University
Princeton, NJ 08544
United States