Sobolev connections and holomorphic structures over Kähler surfaces
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Date
2021-06-15
Publication Type
Journal Article
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yes
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Abstract
In this work we prove that any unitary Sobolev W connection of an Hermitian bundle over a closed Kähler surface whose curvature is (1,1) defines a smooth holomorphic structure. We prove moreover that such a connection can be strongly approximated in any W (p<2) norm by smooth connections satisfying the same integrability condition and consequently carrying smooth holomorphic structures.
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published
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Journal / series
Volume
280 (12)
Pages / Article No.
109003
Publisher
Elsevier
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Subject
Sobolev connections; Holomorphic structures; Variational gauge theory
Organisational unit
03600 - Rivière, Tristan / Rivière, Tristan