English

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 W1,2W^{1,2} connection of an Hermitian bundle over a 2-dimensional K\"ahler manifold whose curvature is (1,1)(1,1) defines a smooth holomorphic structure. We prove moreover that such a connection can be strongly approximated in any W1,pW^{1,p} (p<2p<2) norm by smooth connections satisfying the same integrability condition.

Keywords

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}
}
R2 v1 2026-06-23T11:58:08.731Z