• Corpus ID: 204950534

# Weak Holomorphic Structures over Kähler Surfaces

@article{Punoiu2019WeakHS,
title={Weak Holomorphic Structures over K{\"a}hler Surfaces},
author={Alexandru Păunoiu and Tristan Rivi{\'e}re},
journal={arXiv: Differential Geometry},
year={2019}
}
• Published 29 October 2019
• Mathematics
• arXiv: Differential Geometry
In this work we prove that any unitary Sobolev $W^{1,2}$ connection of an Hermitian bundle over a 2-dimensional Kahler manifold whose curvature is $(1,1)$ defines a smooth holomorphic structure. We prove moreover that such a connection can be strongly approximated in any $W^{1,p}$ ($p<2$) norm by smooth connections satisfying the same integrability condition.

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