Uhlenbeck, K.; Yau, S. T. A note on our previous paper: On the existence of Hermitian Yang-Mills connections in stable vector bundles. (English) Zbl 0678.58041 Commun. Pure Appl. Math. 42, No. 5, 703-707 (1989). 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. Cited in 50 Documents MSC: 58J90 Applications of PDEs on manifolds 53C55 Global differential geometry of Hermitian and Kählerian manifolds 32L05 Holomorphic bundles and generalizations 14L24 Geometric invariant theory Keywords:Yang-Mills; stable vector bundle; Hermitian connection; regularity theory of Yang-Mills connections; regularity of weakly holomorphic maps Citations:Zbl 0615.58045 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Levi, Annali di Mat. Pura ed Appl. 17 3 pp 61– (1910) · JFM 41.0487.01 · doi:10.1007/BF02419336 [2] Rothstein, Math. Zeitschr. 53 pp 84– (1950) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.