Holomorphic Frames for Weakly Converging Holomorphic Vector Bundles
Printed: Mar 2006
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.
57M50 - Geometric structures on low-dimensional manifolds
58E20 - Harmonic maps [See also 53C43], etc.
53C24 - Rigidity results