Weak Holomorphic Structures over K\"ahler Surfaces
Differential Geometry
2019-10-30 v1 Analysis of PDEs
Abstract
In this work we prove that any unitary Sobolev connection of an Hermitian bundle over a 2-dimensional K\"ahler manifold whose curvature is defines a smooth holomorphic structure. We prove moreover that such a connection can be strongly approximated in any () norm by smooth connections satisfying the same integrability condition.
Cite
@article{arxiv.1910.13168,
title = {Weak Holomorphic Structures over K\"ahler Surfaces},
author = {Alexandru Paunoiu and Tristan Rivière},
journal= {arXiv preprint arXiv:1910.13168},
year = {2019}
}