On Extending Calibrations

Abstract: This is a companion note of Zhaa where the extension of local calibration pairs of smooth submanifolds is discussed. Here we emphasize on the case of singular submanifolds. More precisely, we study when a calibration pair around the singular set of a submanifold can extend to a local calibration pair about the entire submanifold. Based upon Zhab several examples of particular interests under the view of calibrated geometry are considered.