On extending calibration pairs
arXiv:1511.03953
Abstract
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 -homologically nontrivial connected submanifold of a smooth Riemannian manifold is homologically mass-minimizing for some metrics in the same conformal class. Moreover, several generalizations for with multiple connected components or for a mutually disjoint collection (see §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.
Improved Version. arXiv admin note: text overlap with arXiv:1501.01836