Uhlenbeck compactness for Yang–Mills flow in higher dimensions

Waldron, Alex

doi:10.1007/s00526-023-02505-7

Calc. Var.

2023

DOI: 10.1007/s00526-023-02505-7

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Uhlenbeck compactness for Yang–Mills flow in higher dimensions

Alex Waldron

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Compactness for $Ω$-Yang-Mills connections

Chen¹,

Wentworth²

2021

Preprint

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On a Riemannian manifold of dimension n we extend the known analytic results on Yang-Mills connections to the class of connections called Ω-Yang-Mills connections, where Ω is a smooth, not necessarily closed, (n − 4)-form on M . Special cases include Ω-anti-selfdual connections and Hermitian-Yang-Mills connections over general complex manifolds. By a key observation, a weak compactness result is obtained for moduli space of smooth Ω-Yang-Mills connections with uniformly L 2 bounded curvature, and it can be improved in the case of Hermitian-Yang-Mills connections over general complex manifolds. A removable singularity theorem for singular Ω-Yang-Mills connections on a trivial bundle with small energy concentration is also proven. As an application, it is shown how to compactify the moduli space of smooth Hermitian-Yang-Mills connections on unitary bundles over a class of balanced manifolds of Hodge-Riemann type. This class includes the metrics coming from multipolarizations, and in particular, the Kähler metrics. In the case of multipolarizations on a projective algebraic manifold, the compactification of smooth irreducible Hermitian-Yang-Mills connections with fixed determinant modulo gauge transformations inherits a complex structure from algebro-geometric considerations.

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Compactness for $Ω$-Yang-Mills connections

Chen¹,

Wentworth²

2021

Preprint

View full text Add to dashboard Cite

show abstract

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Uhlenbeck compactness for Yang–Mills flow in higher dimensions

Cited by 1 publication

References 30 publications

Compactness for $Ω$-Yang-Mills connections

Compactness for $Ω$-Yang-Mills connections

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