Geodesic
A Compactness Theorem for Yang-Mills Connections
Canadian mathematical bulletin, Tome 47 (2004) no. 4, pp. 624-634

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we consider Yang-Mills connections on a vector bundle $E$ over a compact Riemannian manifold $M$ of dimension $m\,>\,4$ , and we show that any set of Yang-Mills connections with the uniformly bounded ${{L}^{\frac{m}{2}}}$ -norm of curvature is compact in ${{C}^{\infty }}$ topology.
DOI : 10.4153/CMB-2004-060-x
Mots-clés : 58E20, 53C21, Yang-Mills connection, vector bundle, gauge transformation 
Zhang, Xi. A Compactness Theorem for Yang-Mills Connections. Canadian mathematical bulletin, Tome 47 (2004) no. 4, pp. 624-634. doi: 10.4153/CMB-2004-060-x
@article{10_4153_CMB_2004_060_x,
     author = {Zhang, Xi},
     title = {A {Compactness} {Theorem} for {Yang-Mills} {Connections}},
     journal = {Canadian mathematical bulletin},
     pages = {624--634},
     year = {2004},
     volume = {47},
     number = {4},
     doi = {10.4153/CMB-2004-060-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-060-x/}
}
TY  - JOUR
AU  - Zhang, Xi
TI  - A Compactness Theorem for Yang-Mills Connections
JO  - Canadian mathematical bulletin
PY  - 2004
SP  - 624
EP  - 634
VL  - 47
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-060-x/
DO  - 10.4153/CMB-2004-060-x
ID  - 10_4153_CMB_2004_060_x
ER  - 
%0 Journal Article
%A Zhang, Xi
%T A Compactness Theorem for Yang-Mills Connections
%J Canadian mathematical bulletin
%D 2004
%P 624-634
%V 47
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-060-x/
%R 10.4153/CMB-2004-060-x
%F 10_4153_CMB_2004_060_x

[1] [1] Uhlenbeck, K. K., Removable singularities in Yang-Mills fields. Comm. Math. Phys. 83 (1982), 11–29. Google Scholar

[2] [2] Uhlenbeck, K. K., Connections with Lp bounds on curvature. Comm. Math. Phys. 83 (1982), 31–42. Google Scholar

[3] [3] Nakajima, H., Compactness of the moduli space of Yang-Mills connections in higher dimensions. J. Math. Soc. Japan 40 (1988), 383–392. Google Scholar

[4] [4] Tian, G., Gauge theory and calibrated geometry. Ann.Math. 151 (2000), 193–208. Google Scholar

[5] [5] Price, P., A monotonicity formula for Yang-Mills fields. Manuscripta Math. 43 (1983), 131–166. Google Scholar

[6] [6] Sibner, L. M., The isolated point singularity problem for the coupled Yang-Mills eqaution in higher dimensions. Math. Ann. 271 (1985), 125–131. Google Scholar

Cité par Sources :