On Gap Properties and Instabilities of $p$-Yang--Mills Fields

http://dx.doi.org/10.4153/CJM-2007-053-x
Canad. J. Math. 59(2007), 1245-1259

  Published:2007-12-01
 Printed: Dec 2007

We consider the $p$-Yang--Mills functional $(p\geq 2)$ defined as $\YM_p(\nabla):=\frac 1 p \int_M \|\rn\|^p$. We call critical points of $\YM_p(\cdot)$ the $p$-Yang--Mills connections, and the associated curvature $\rn$ 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 $\mathbb{S}^{n+k}$.