Pseudo-holomorphic curves and the Weinstein conjecture

TL;DR

This paper proves the existence of periodic Reeb orbits in certain tight contact structures on closed 3-manifolds, leveraging symplectic geometry and a key theorem by Cliff Taubes.

Contribution

It establishes the existence of periodic Reeb orbits for a broad class of tight contact structures, including Stein fillable ones, using pseudo-holomorphic curves.

Findings

Existence of periodic Reeb orbits in tight contact structures.

Application of Taubes' theorem to contact topology.

Extension to Stein fillable structures.

Abstract

We established existence of periodic Reeb orbits for a large class of tight contact structures on closed 3-manifolds, notably the Stein fillable structures, based on a fundamental theorem of Cliff Taubes on symplectic 4-manifolds.