On Regularity of J-holomorphic Maps

TL;DR

This paper proves that L^2_1 and J-holomorphic curves are smooth and establishes a removal of singularity theorem for finite energy curves, simplifying regularity results in symplectic geometry.

Contribution

It offers a concise proof of regularity for J-holomorphic maps and applies it to remove singularities in finite energy cases, advancing understanding in symplectic topology.

Findings

L^2_1 J-holomorphic curves are smooth

Removal of singularities for finite energy J-holomorphic curves

Simplified proof technique for regularity

Abstract

We provide a short proof that an $L^2_1$ and $J$-holomorphic curve is in fact smooth. As an application, we deduce a removal of singularity theorem for curves of finite energy.