Weak Holomorphic Structures over Kähler Surfaces

Abstract

In this work we prove that any unitary Sobolev $W^{1,2}$ connection of an Hermitian bundle over a 2-dimensional Kähler 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.

References in corpus (1)

• The Space of Weak Connections in High Dimensions