As part of his theory of symbolic extensions for topological $\mathbb{R}$-flows Burguet (2019) introduced the small flow boundary property (SFBP). This property played a key role in our solution of the Bowen and Walters (1972) problem on expansive flows. However, the relation between SFBP and mean dimension remained a mystery. In this talk I will give a detailed proof that an aperiodic flow with SFBP has zero mean dimension.
The proof is very different from the analogous result for $\mathbb{Z}$ actions by Lindenstrauss and Weiss (2000). Joint work with Ruxi Shi.