Critical Values of Calibrations and MinimalSubmanifolds

2015-01-05
On a calibrated manifold M with differential p-form ϕ as the calibration, calibrated submanifolds i.e. ϕ-submanifolds are globally volume minimizing in their homology classes. Thus, they are a very good source of minimal submanifolds. These are the submanifolds corresponding to the global maximum value of the calibration ϕ when considered as a function on Grassmannian bundle of oriented p-planes of M. In this talk, I will explain that submanifolds corresponding to any non-zero critical value of a calibration, namely ϕ-critical submanifolds, are also minimal under some additional conditions about either the calibration ϕ or the critical value. Furthermore, I will give some examples of ϕ-critical submanifolds.

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Citation Formats
İ. Ünal, “Critical Values of Calibrations and MinimalSubmanifolds,” presented at the 2015 Joint Mathematics Meetings, San Antonio, (10 - 13 Ocak 2015), 2015, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/73721.