  Let $(Y,g)$ be a compact Riemannian manifold of positive scalar curvature
(psc). It is well-known, due to Schoen-Yau, that any closed stable minimal
hypersurface of $Y$ also admits a psc-metric. We establish an analogous result
for stable minimal hypersurfaces with free boundary. Furthermore, we combine
this result with tools from geometric measure theory and conformal geometry to
study psc-bordism. For instance, assume $(Y_0,g_0)$ and $(Y_1,g_1)$ are closed
psc-manifolds equipped with stable minimal hypersurfaces $X_0 \subset Y_0$ and
$X_1\subset Y_1$. Under natural topological conditions, we show that a
psc-bordism $(Z,\bar g) : (Y_0,g_0)\rightsquigarrow (Y_1,g_1)$ gives rise to a
psc-bordism between $X_0$ and $X_1$ equipped with the psc-metrics given by the
Schoen-Yau construction.
