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On gap properties and instabilities of \(p\)-Yang-Mills fields. (English) Zbl 1131.58010

Summary: We consider the \(p\)-Yang-Mills functional \((p\geq 2)\) defined as \(YM_p(\nabla):= \frac1p\int_M\|R^\nabla\|^p\). We call critical points of \(YM_p(\cdot)\) the \(p\)-Yang-Mills connections, and the associated curvature \(R^\nabla\) the \(p\)-Yang-Mills fields.
In this paper, we prove gap properties and instability theorems for \(p\)-Yang-Mills fields over submanifolds in \(\mathbb R^{n+k}\) and \(\mathbb S^{n+k}\).

MSC:

58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
53C05 Connections (general theory)
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