A Geometric Proof of Removal of Boundary Singularities of Pseudo-Holomorphic Curves

2012/10/16 by Urs Fuchs, Fuchs, Urs, Lizhen Qin +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG

paper · pdf · doi:10.48550/arxiv.1210.4324

Any comments are welcome

arxiv created 2012/10/16 · arxiv updated 2012/10/17

Abstract

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.

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