Growth-fragmentation processes in Brownian motion indexed by the Brownian tree

We consider the model of Brownian motion indexed by the Brownian tree. For every r.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.