Keywords: exponential Yang-Mills field; energy gap
@article{10_5817_AM2018_3_127,
author = {Zhou, Zhen-Rong},
title = {Energy gaps for exponential {Yang-Mills} fields},
journal = {Archivum mathematicum},
pages = {127--134},
year = {2018},
volume = {54},
number = {3},
doi = {10.5817/AM2018-3-127},
mrnumber = {3847320},
zbl = {06940793},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2018-3-127/}
}
Zhou, Zhen-Rong. Energy gaps for exponential Yang-Mills fields. Archivum mathematicum, Tome 54 (2018) no. 3, pp. 127-134. doi: 10.5817/AM2018-3-127
[1] Beckner, W.: Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality. Ann. of Math. (2) 138 (1993), 213–242. | MR
[2] Bourguignon, J.P., Lawson, H.B.: Stability and isolation phenomena for Yang-Mills fields. Comm. Math. Phys. 79 (2) (1981). | DOI | MR
[3] Bourguignon, J.P., Lawson, H.B., Simons, J.: Stability and gap phenomena for Yang-Mills fields. Proc. Natl. Acad. Sci. USA 76 (1979). | DOI | MR | Zbl
[4] Chen, Q., Zhou, Z.R.: On gap properties and instabilities of p-Yang-Mills fields. Canad. J. Math. 59 (6) (2007), 1245–1259. | DOI | MR | Zbl
[5] Dodziuk, J., Min-Oo, : An $L_{2}$-isolation theorem for Yang-Mills fields over complete manifolds. Compositio Math 47 (2) (1982), 165–169. | MR
[6] Donaldson, S.K., Kronheimer, P.B.: The geometry of four-manifolds. Proceedings of Oxford Mathematical Monographs, The Clarendon Press, Oxford University Pres, Oxford Science Publications, New York, 1990. | MR
[7] Feehan, P.M.N.: Energy gap for Yang-Mills connections, I: Four-dimensional closed Riemannian manifold. Adv. Math. 296 (2016), 55–84. | DOI | MR
[8] Feehan, P.M.N.: Energy gap for Yang-Mills connections, II: Arbitrary closed Riemannian manifolds. Adv. Math. 312 (2017), 547–587. | DOI | MR
[9] Gerhardt, C.: An energy gap for Yang-Mills connections. Comm. Math. Phys. 298 (2010), 515–522. | DOI | MR
[10] Hebey, E.: Sobolev spaces on Riemannian manifolds. Lecture Notes in Math., vol. 1635, Springer-Verlag Berlin Heidelberg, 1996. | MR
[11] Min-Oo, : An $L_{2}$-isolation theorem for Yang-Mills fields. Compositio Math. 47 (2) (1982), 153–163. | MR
[12] Shen, C.L.: The gap phenomena of Yang-Mills fields over the complete manifolds. Math. Z. 180 (1982), 69–77. | DOI | MR
[13] Zhou, Z.R.: Inequalities of Simons type and gaps for Yang-Mills fields. Ann. Global Anal. Geom. 48 (3) (2015), 223–232. | DOI | MR
[14] Zhou, Z.R.: Energy gaps for Yang-Mills fields. J. Math. Anal. Appl. 439 (2016), 514–522. | DOI | MR
[15] Zhou, Z.R., Chen Qun, : Global pinching lemmas and their applications to geometry of submanifolds, harmonic maps and Yang-Mills fields. Adv. Math. 32 (1) (2003), 319–326. | MR
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