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# Holomorphic Frames for Weakly Converging Holomorphic Vector Bundles

Published:2006-03-01
Printed: Mar 2006
• Richard A. Wentworth
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## Abstract

Using a modification of Webster's proof of the Newlander--Nirenberg theorem, it is shown that, for a weakly convergent sequence of integrable unitary connections on a complex vector bundle over a complex manifold, there is a subsequence of local holomorphic frames that converges strongly in an appropriate Holder class.
 MSC Classifications: 57M50 - Geometric structures on low-dimensional manifolds 58E20 - Harmonic maps [See also 53C43], etc. 53C24 - Rigidity results