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Title:
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Minimizers of the vector-valued coarea formula |
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Author:
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Carroll, Colin |
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Advisor:
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Hardt, Robert |
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Degree:
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Doctor of Philosophy thesis |
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Abstract:
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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. |
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Citation:
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Carroll, Colin. "Minimizers of the vector-valued coarea formula." Doctoral Thesis, Rice University, May, 2012. ETD http://hdl.handle.net/1911/64635. |
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Citable link to this page:
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http://hdl.handle.net/1911/64635 |
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Date:
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2012-09-05 |
