Energy gaps for exponential Yang-Mills fields
Archivum mathematicum, Tome 54 (2018) no. 3, pp. 127-134 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, some inequalities of Simons type for exponential Yang-Mills fields over compact Riemannian manifolds are established, and the energy gaps are obtained.
In this paper, some inequalities of Simons type for exponential Yang-Mills fields over compact Riemannian manifolds are established, and the energy gaps are obtained.
DOI : 10.5817/AM2018-3-127
Classification : 58E15, 58E20
Keywords: exponential Yang-Mills field; energy gap
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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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