The vector-valued coarea formula provides a relationship between the integral of the Jacobian of a map from high dimensions down to low dimensions with the integral over the measure of the fibers of this map. We explore minimizers of this functional, proving existence using both a variational approach and an approach with currents. Additionally, we consider what properties these minimizers will have and provide examples. Finally, this problem is considered in metric spaces, where a third existence proof is given.
| Identifer | oai:union.ndltd.org:RICE/oai:scholarship.rice.edu:1911/64635 |
| Date | 06 September 2012 |
| Creators | Carroll, Colin |
| Contributors | Hardt, Robert |
| Source Sets | Rice University |
| Language | English |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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