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.