Minimizers of Higher Order Gauge Invariant Functionals |
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Authors: | Andreas Gastel Christoph Scheven |
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Institution: | 1.Fakult?t für Mathematik,Universit?t Duisburg-Essen,Essen,Germany |
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Abstract: | We introduce higher order variants of the Yang–Mills functional that involve \((n-2)\)-th order derivatives of the curvature. We prove coercivity and smoothness of critical points in Uhlenbeck gauge in dimensions \(\mathrm {dim}M\le 2n\). These results are then used to establish the existence of smooth minimizers on a given principal bundle \(P\rightarrow M\) for subcritical dimensions \(\mathrm {dim}M<2n\). In the case of critical dimension \(\mathrm {dim}M=2n\) we construct a minimizer on a bundle which might differ from the prescribed one, but has the same Chern classes \(c_1,\ldots ,c_{n-1}\). 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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