  We prove a sharp area estimate for catenoids that allows us to rule out the
phenomenon of multiplicity in min-max theory in several settings. We apply it
to prove that i) the width of a three-manifold with positive Ricci curvature is
realized by an orientable minimal surface ii) minimal genus Heegaard surfaces
in such manifolds can be isotoped to be minimal and iii) the "doublings" of the
Clifford torus by Kapouleas-Yang can be constructed variationally by an
equivariant min-max procedure. In higher dimensions we also prove that the
width of manifolds with positive Ricci curvature is achieved by an index 1
orientable minimal hypersurface.
