Exponential Convergence to Non-degenerate Reeb Chords

TL;DR

This paper proves exponential convergence results for holomorphic curves in symplectizations of contact manifolds with Legendrian boundary, extending previous dimension-specific work to all dimensions.

Contribution

It generalizes exponential convergence results for holomorphic curves to higher dimensions, broadening the scope of earlier dimension 3 findings.

Findings

Exponential convergence of holomorphic curves established in all dimensions.

Results apply to symplectizations with Legendrian boundary.

Generalization of prior dimension-specific results.

Abstract

Exponential convergence type results are proved for holomorphic curves in the symplectization of a contact manifold $Y$ with boundary on a Legendrian cylinder. The results are proven in all dimensions, and generalize earlier work specific to dimension 3.