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Minimizers of the vector-valued coarea formula

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Title: Minimizers of the vector-valued coarea formula
Author: Carroll, Colin
Advisor: Hardt, Robert M.
Degree: Doctor of Philosophy thesis
Abstract: 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.
Citation: Carroll, Colin. (2012) "Minimizers of the vector-valued coarea formula." Doctoral Thesis, Rice University. http://hdl.handle.net/1911/64635.
URI: http://hdl.handle.net/1911/64635
Date: 2012-09-05

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