Comptes Rendus
no. 8
Differential geometry/Mathematical physics
A proof of energy gap for Yang–Mills connections
[Une preuve du gap d'énergie pour les connexions de Yang–Mills]

Présenté par : the Editorial Board

Teng Huang1
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
Comptes Rendus. Mathématique, Volume 355 (2017) no. 8, pp. 910-913.

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.

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).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.07.012
Teng Huang 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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Teng Huang. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.07.012/

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

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

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

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

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

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