Abstract
In this paper, we establish an inequality of Simons type for Yang–Mills fields, and obtain a gap property, which generalize the results obtained in Bourguignon and Lawson (Comm Math Phys 79(2):189–230, 1981).
Similar content being viewed by others
References
Bourguignon, J.P., Lawson, H.B.: Stability and isolation phenomena for Yang-Mills fields. Comm. Math. Phys. 79(2), 189–230 (1981)
Bourguignon, J.P., Lawson, H.B., Simons, J.: Stability and gap phenomena for Yang–Mills fields. Proc. Acad. Sci. USA 76, 1550–1553 (1979)
Chen, Q., Zhou, Z.R.: On gap properties and instabilities of \(p\)-Yang–Mills fields. Can. J. Math. 59(6), 1245–1259 (2007)
Dodziuk, J., Min-Oo, M.: An \(L_{2}\)-isolation theorem for Yang–Mills fields over complete manifolds. Compositio Math. 47, 165–169 (1982)
Donaldson, S.K., Kronheimer, P.B.: The geometry of four-manifolds. In: Proceedings of Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford Science Publications, New York (1990)
Gantmacher, F.R.: The Theory of Matrices, AMS Chelsea Publishing, American Mathematical Society Providence, Rhode Island (2000)
Gerhardt, C.: An energy gap for Yang–Mills connections. Comm. Math. Phys. 298, 515–522 (2010)
Jia, G.Y., Zhou, Z.R.: Stability of F-Yang–Mills fields on submanifolds. Arch. Math. 49, 125–139 (2013)
Jia, G.Y., Zhou, Z.R.: Gaps of F-Yang–Mills fields on submanifolds. Tsukuba J. Math. 36(1), 121–134 (2012)
Min-Oo, M.: An \(L_{2}\)-isolation theorem for Yang–Mills fields. Compositio Math. 47(2), 153–163 (1982)
Price, P.: A monotonicity formula for Yang–Mills fields. Manuscr. Math. 43, 131–166 (1983)
Shen, C.L.: The gap phenomena of Yang–Mills fields over the complete manifolds. Math. Z. 180, 69–77 (1982)
Simons, J.: Minimal varieties in Riemannian manifolds. Ann. Math. 88, 62–105 (1968)
Uhlenbeck, K.: Connections with \(L^{p}\) bounds on curvature. Comm. Math. Phys. 83, 31–42 (1982)
Xin, Y.L.: Instability theorems of Yang–Mills fields. Acta Math. Sci. 3(1) 103–112 (1983)
Zhou, Z.R., Qun, C.: Global pinching lemmas and their applications to geometry of submanifolds, harmonic maps and Yang–Mills fields. Adv Math. (PRC) 32(3), 319–326
Author information
Authors and Affiliations
Corresponding author
Additional information
Research supported by National Science Foundation of China No. 10871149.
Rights and permissions
About this article
Cite this article
Zhou, ZR. Inequalities of Simons type and gaps for Yang–Mills fields. Ann Glob Anal Geom 48, 223–232 (2015). https://doi.org/10.1007/s10455-015-9467-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10455-015-9467-z