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

Published online by Cambridge University Press:  20 November 2018

Qun Chen  and
Zhen-Rong Zhou
Qun Chen
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China email: qunchen@whu.edu.cn
Zhen-Rong Zhou
Affiliation:
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China email: zrzhou@mail.ccnu.edu.cn
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Abstract

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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 ${{\mathbb{S}}^{n+k}}$.

Keywords

58E1553C05p-Yang–Mills fieldgap propertyinstabilitysubmanifold
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 6 , 01 December 2007 , pp. 1245 - 1259
Copyright
Copyright © Canadian Mathematical Society 2007

References

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