  The paper studies how to extend local calibration pairs to global ones in
various situations. As a result, new discoveries involving mass-minimizing
properties are exhibited. In particular, we show that a $\mathbb
R$-homologically nontrivial connected submanifold $M$ of a smooth Riemannian
manifold $X$ is homologically mass-minimizing for some metrics in the same
conformal class. Moreover, several generalizations for $M$ with multiple
connected components or for a mutually disjoint collection (see {\S}3.5) are
obtained. For a submanifold with certain singularities, we also establish an
extension theorem for generating global calibration pairs. By combining these
results, we find that, in some Riemannian manifolds, there are homologically
mass-minimizing smooth submanifolds which cannot be calibrated by any smooth
calibration.
