Schwarz Reflection Principle, Boundary Regularity and Compactness for J-Complex Curves

TL;DR

This paper extends the Schwarz Reflection Principle to J-complex discs in almost complex manifolds, providing boundary regularity results and precise Gromov compactness convergence in analytic settings.

Contribution

It establishes the Schwarz Reflection Principle for J-complex discs attached to real analytic J-totally real submanifolds and proves boundary regularity and convergence results in analytic classes.

Findings

Schwarz Reflection Principle holds for J-complex discs in real analytic settings.

Boundary regularity of J-complex discs is precisely characterized.

Gromov compactness convergence is established in C^{k,α} classes.

Abstract

We establish the Schwarz Reflection Principle for $J$-complex discs attached to a real analytic $J$-totally real submanifold of an almost complex manifold with real analytic $J$. We also prove the precise boundary regularity and derive the precise convergence in Gromov compactness theorem in $\calc^{k,\alpha}$-classes.