Search: All articles in the CJM digital archive with keyword $p$-Yang--Mills field
 On Gap Properties and Instabilities of $p$-Yang--Mills Fields 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 $\mathbb{S}^{n+k}$. Keywords:$p$-Yang--Mills field, gap property, instability, submanifoldCategories:58E15, 53C05