For an Alexandrov space, we can define recursively the boundary subset, which might be empty. It is conjectured that this subset equipped with the induced metric is also an Alexandrov space. By the work of Grove, Moreno, and Petersen, this conjecture holds when the Alexandrov space is the leaf space of a singular Riemannian foliation.

In this talk, for a manifold with a singular Riemannian foliation, we present sufficient conditions on the foliation and the geometry of the manifold to guarantee the existence of boundary points in the leaf space. For this, we extend ideas for group actions, which allows us to reduce the foliation to a new lower dimensional foliated space.

This work is joint with A. Moreno.