A note on our previous paper: On the existence of Hermitian Yang-Mills connections in stable vector bundles. (English) Zbl 0678.58041

In our paper [ibid. 38, 755-768 (1985; Zbl 0615.58045)], we present two different proofs of the main theorem. The first proof depends on the regularity theory of Yang-Mills connections. The second one depends on the regularity of weakly holomorphic maps. It turns out that the second proof contains a gap (Lemma 6.2 is incorrect) and we shall close this gap in this note. Both the gap and the correction were found right after the paper was in print. We regret this error.


58J90 Applications of PDEs on manifolds
53C55 Global differential geometry of Hermitian and Kählerian manifolds
32L05 Holomorphic bundles and generalizations
14L24 Geometric invariant theory


Zbl 0615.58045
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[1] Levi, Annali di Mat. Pura ed Appl. 17 3 pp 61– (1910) · JFM 41.0487.01
[2] Rothstein, Math. Zeitschr. 53 pp 84– (1950)
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