Weak Holomorphic Structures over K\"ahler Surfaces

Alexandru Paunoiu; Tristan Rivière

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arXiv · 1910.13168

Weak Holomorphic Structures over K\"ahler Surfaces

Alexandru Paunoiu·Tristan Rivière

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Abstract

In this work we prove that any unitary Sobolev $W^{1,2}$ connection of an Hermitian bundle over a 2-dimensional K\"ahler 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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Alexandru Paunoiu, Tristan Rivière. 2019-10-29. Weak Holomorphic Structures over K\"ahler Surfaces. https://arxiv.org/abs/1910.13168

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