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On Gap Properties and Instabilities of p-Yang–Mills Fields
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- Journal:
- Canadian Journal of Mathematics / Volume 59 / Issue 6 / 01 December 2007
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1245-1259
- Print publication:
- 01 December 2007
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- Article
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We consider the
$p$-Yang-Mills functional 
$\left( p\,\ge \,2 \right)$ defined as 
$Y{{M}_{p}}(\nabla ):=\frac{1}{p}{{\int }_{M}}{{\left\| {{R}^{\nabla }} \right\|}^{p}}$. We call critical points of 
$Y{{M}_{p}}(\cdot )$ 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 
${{\mathbb{S}}^{n+k}}$.
