Differential geometry/Mathematical physics
A proof of energy gap for Yang–Mills connections
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 910-913.

In this note, we prove an Ln2-energy gap result for Yang–Mills connections on a principal G-bundle over a compact manifold without using the Lojasiewicz–Simon gradient inequality ([2] Theorem 1.1).

Dans cette note, nous démontrons un résultat concernant le gap d'énergie Ln2 pour les connexions de Yang–Mills sur un fibré principal de groupe structural G sur une variété compacte, sans utiliser l'inégalité du gradient de Lojasiewicz–Simon.

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DOI: 10.1016/j.crma.2017.07.012
Huang, Teng 1

1 Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, PR China
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Huang, Teng. A proof of energy gap for Yang–Mills connections. Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 910-913. doi : 10.1016/j.crma.2017.07.012. http://www.numdam.org/articles/10.1016/j.crma.2017.07.012/

[1] Donaldson, S.K.; Kronheimer, P.B. The Geometry of Four-Manifolds, Oxford University Press, 1990

[2] Feehan, P.M.N. Energy gap for Yang–Mills connections, II: arbitrary closed Riemannian manifolds, Adv. Math., Volume 312 (2017), pp. 547-587

[3] Gerhardt, C. An energy gap for Yang–Mills connections, Commun. Math. Phys., Volume 298 (2010), pp. 515-522

[4] Uhlenbeck, K.K. Removable singularities in Yang–Mills fields, Commun. Math. Phys., Volume 83 (1982), pp. 11-29

[5] Uhlenbeck, K.K. The Chern classes of Sobolev connections, Commun. Math. Phys., Volume 101 (1985), pp. 445-457

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