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Some Energy Properties of Yang-Mills Connections

Differential Geometry 2016-06-15 v3 Mathematical Physics math.MP

Abstract

We consider a vector bundle EE over a compact Riemannian manifold MM=MnM^{n},n4n\geq 4,and AA is a Yang-Mills connection with Ln2L^{\frac{n}{2}} curvature FAF_{A} on EE.Then we prove a mean value inequality for the density FAn2|F_{A}|^{\frac{n}{2}}.This inequality give rise to an energy concentrate principle for sequences of solutions that have bounded energy.We also proof that the energy must be bounded from below by some positive constant unless EE is a flat bundle.

Keywords

Cite

@article{arxiv.1502.03198,
  title  = {Some Energy Properties of Yang-Mills Connections},
  author = {Teng Huang},
  journal= {arXiv preprint arXiv:1502.03198},
  year   = {2016}
}

Comments

This paper has been withdrawn. The result of this paper turned out to be a special case of arXiv:1502.00668