TL;DR
This paper explores conditions under which calibration pairs around singular submanifolds can be extended to the entire submanifold, expanding the understanding of calibrated geometry in singular contexts.
Contribution
It extends previous work on calibration pairs to include singular submanifolds and provides examples illustrating these extensions.
Findings
Conditions identified for extending calibration pairs to singular submanifolds
Examples demonstrating the application of these extension conditions
Enhanced understanding of calibrated geometry in singular settings
Abstract
This is a companion note of [Zhaa] (arXiv:1501.01836) 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] (arXiv:1501.04681) several examples of particular interests under the view of calibrated geometry are considered.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Point processes and geometric inequalities