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On Gap Properties and Instabilities of p-Yang–Mills Fields
Published online by Cambridge University Press: 20 November 2018
Abstract
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 ${{\mathbb{S}}^{n+k}}$.
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- Copyright © Canadian Mathematical Society 2007
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