On closed characteristics of minimal action on a convex three-sphere

TL;DR

This paper proves that on convex three-spheres, minimal action closed characteristics bound disk-like surfaces, linking symplectic capacity with minimal action, advancing understanding of convex boundary dynamics.

Contribution

It establishes the existence of disk-like global surfaces of section for minimal action closed characteristics on convex three-spheres, connecting symplectic capacity with boundary dynamics.

Findings

Every minimal action closed characteristic bounds a disk-like global surface of section.

The cylindrical symplectic capacity equals the minimal action of a closed characteristic.

Provides new insights into the dynamics of convex three-spheres.

Abstract

We prove that every closed characteristic of minimal action on the boundary of a uniformly convex domain in $\R^4$ bounds a disk-like global surface of section. A corollary is that the cylindrical symplectic capacity of a convex body in $\R^4$ coincides with the minimal action of a closed generalized characteristic on its boundary.