Browsing by Author "Carroll, Colin"
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Item Minimizers of the vector-valued coarea formula(2012-09-05) Carroll, Colin; Hardt, Robert M.; Wolf, Michael; Cox, Steven J.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.