Global surfaces of section with positive genus for dynamically convex Reeb flows

TL;DR

This paper proves new existence results for global surfaces of section with positive genus in dynamically convex Reeb flows on the three-sphere, using a combination of pseudo-holomorphic curve and ergodic methods.

Contribution

It introduces novel techniques to establish the existence of genus-positive global surfaces of section in a specific dynamical setting.

Findings

Existence of genus-positive global surfaces of section for certain Reeb flows

Application of pseudo-holomorphic curve methods to dynamical systems

Integration of ergodic methods with geometric analysis

Abstract

We establish some new existence results for global surfaces of section of dynamically convex Reeb flows on the three-sphere. These sections often have genus, and are the result of a combination of pseudo-holomorphic curve methods with some elementary ergodic methods.