## 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)
Full Text: