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

  Published:2007-12-01
 Printed: Dec 2007
  • Qun Chen
  • Zhen-Rong Zhou
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Abstract

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, submanifold $p$-Yang--Mills field, gap property, instability, submanifold
MSC Classifications: 58E15, 53C05 show english descriptions Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.
Connections, general theory
58E15 - Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.
53C05 - Connections, general theory
 

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