Finite extinction time of a family of homogeneous Ricci flows

We show that for a broad family of noncompact homogeneous Riemannian manifolds, the corresponding homogeneous Ricci flow solutions have finite extinction time, thereby confirming the dynamical Alekseevskii conjecture for these spaces. As an application, we prove that on such homogeneous manifolds $G\mathrm{/}H$, the space of all $G$-invariant positive scalar curvature metrics is contractible.