A Geometric Proof of Removal of Boundary Singularities of   Pseudo-Holomorphic Curves
  We prove two theorems on the removal of singularities on the boundary of a pseudo-holomorphic curve. In one theorem, we need no apriori assumption on the area of the curve. The proof uses a doubling argument with the goal of converting curves with boundary to curves without boundary. Our method is new and geometric and it does not need Sobolev spaces and PDEs. 
Urs Fuchs, Lizhen Qin
math.SG math.DG