Abstract
Let A be a connection of a principal bundle P over a Riemannian manifold M, such that its curvature
is monotonically increasing in r, for some c depending only on the local geometry of M. We are interested in the singular set defined by
A Appendix
We give the proof of Theorem 4.2.
The proof is by contradiction. Suppose the contrary holds. Then there exist an
Up to passing to a subsequence we may assume
Let us choose
On the other hand, let
where we denoted
By (A.1), (A.3), the fact that
From (A.2) and (A.4), we see that
Acknowledgements
The author gratefully thanks his advisor A. Naber for interesting him in the problem and giving him constant support and encouragements. The author would also like to thank the anonymous referee for pointing out an issue in an earlier draft.
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