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Session 11. Geometric Analysis and Related Topics
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Minimizers of higher order gauge invariant functionals |
Andreas Gastel, Universität Duisburg-Essen, Germany
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This is joint work with Christoph Scheven, Duisburg-Essen
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We introduce higher order variants of the Yang-Mills functional
that involve \((n-2)\)th order derivatives of the curvature.
We discuss coercivity up to gauge transformations, existence of Uhlenbeck
gauges, existence and smoothness of minimizers in the critical dimension.
A key result is a removable singularity theorem for
bundles carrying a \(W^{n-1,2}\)-connection. This generalizes a recent
result by Petrache and Rivière.
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