Coarse hyperbolicity and closed orbits for quasigeodesic flows

TL;DR

This paper proves a conjecture that every quasigeodesic flow on a closed hyperbolic 3-manifold contains closed orbits, confirming a significant aspect of the flow's dynamical structure.

Contribution

It establishes that all quasigeodesic flows on closed hyperbolic 3-manifolds have closed orbits, resolving Calegari's conjecture.

Findings

All quasigeodesic flows on closed hyperbolic 3-manifolds have closed orbits

Provides new insights into the dynamics of flows on hyperbolic 3-manifolds

Confirms a long-standing conjecture in the field

Abstract

We prove Calegari's conjecture that every quasigeodesic flow on a closed hyperbolic 3-manifold has closed orbits.