Biquard, Olivier Extension of a hermitian holomorphic fiber bundle with \(L^ p\) curvature over an open curve. (Prolongement d’un fibré holomorphe hermitien a courbure \(L^ p\) sur une courbe ouverte.) (French. English summary) Zbl 0764.32008 Int. J. Math. 3, No. 4, 441-453 (1992). Let \(X\) be a Riemann surface, \(S\) be a finite subset of \(X\), and \({\mathcal E}\to X\backslash S\) be a hermitian holomorphic fiber bundle with \(L^ p\)-curvature \((p>1)\). It is studied the asymptotic behaviour of the Chern connection around the points of \(S\). It is given a solution of \(\overline\partial\)-problem in a weighted Sobolev space. As consequence, the author extends the holomorphic structure of \({\mathcal E}\) over \(S\) to get a parabolic bundle, and gives a classification of such hermitian metrics. Reviewer: A.Pankov (Vinnitsa) Cited in 4 Documents MSC: 32Q20 Kähler-Einstein manifolds Keywords:hermitian holomorphic fiber bundle with \(L^ p\)-curvature; \(\overline\partial\)-problem; Chern connection; weighted Sobolev space; parabolic bundle; hermitian metrics PDFBibTeX XMLCite \textit{O. Biquard}, Int. J. Math. 3, No. 4, 441--453 (1992; Zbl 0764.32008) Full Text: DOI