We consider the model of Brownian motion indexed by the Brownian tree. For every $r\geq 0$ and every connected component of the set of points where Brownian motion is greater than $r$, we define the boundary size of this component, and we then show that the collection of these boundary sizes evolves when $r$ varies like a well-identified growth-fragmentation process. We then prove that the same growth-fragmentation process appears when slicing a Brownian disk at height $r$ and considering the perimeters of the resulting connected components.
"Growth-fragmentation processes in Brownian motion indexed by the Brownian tree." Ann. Probab. 48 (4) 1742 - 1784, July 2020. https://doi.org/10.1214/19-AOP1406