We will prove an upper bound for the volume of a minimal hypersurface in a closed Riemannian manifold conformally equivalent to a manifold with Ric > -(n-1). In the second part of the talk we will construct a sweepout of a closed 3-manifold with positive Ricci curvature by 1-cycles of controlled length and prove an upper bound for the length of a stationary geodesic net. These are joint works with Parker Glynn-Adey (Toronto) and Xin Zhou (MIT).