Let $X$ be a reduced $n$-dimensional complex space, for which the set of singularities consists of finitely many points. If $X^{\text{'}}\subseteq X$ denotes the set of smooth points, the author considers a holomorphic vector bundle $E\to X^{\text{'}}\setminus A$, equipped with a Hermitian metric $h$, where $A$ represents a closed analytic subset of complex codimension at least two. The results, surveyed in this paper, provide criteria for holomorphic extension of $E$ across $A$, or across the singular points of $X$ if $A=⌀$. The approach taken here is via the metric $h$, and in particular via the $L^2$-theory of the Cauchy-Riemann equation on a punctured neighbourhood for differential $(p,q)$-forms with coefficients in $E$ .

EUDML-ID : urn:eudml:doc:221612
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@article{701690,
     title = {A survey of boundary value problems for bundles over complex spaces},
     booktitle = {Proceedings of the 21st Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2002},
     pages = {[89]-95},
     mrnumber = {MR1972427},
     zbl = {1013.32023},
     url = {http://dml.mathdoc.fr/item/701690}
}

Harris, Adam. A survey of boundary value problems for bundles over complex spaces, dans Proceedings of the 21st Winter School "Geometry and Physics", GDML_Books,  (2002), pp. [89]-95. http://gdmltest.u-ga.fr/item/701690/