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

TL;DR

This paper introduces a new geometric method to prove boundary singularity removal for pseudo-holomorphic curves, eliminating the need for area assumptions or PDE techniques.

Contribution

It provides a novel geometric proof for boundary singularity removal without relying on Sobolev spaces or PDEs, broadening the theoretical toolkit.

Findings

Proves boundary singularity removal without area assumptions

Uses a doubling argument to convert boundary curves to boundaryless curves

Introduces a new geometric method independent of PDEs

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.