|
Let X be a complex n-dimensional reduced analytic space with isolated singular point x0,and with a strongly plurisubharmonic function p : X --> [0;∞) such that p(x0) = 0.A smooth Kähler form on X {x0} is then defined by i p.The associated metric is assumed to have Lnloc-curvature, toadmit the Sobolev inequality and to have suitable volume growth near x0.Let E --> X {x0} be a Hermitian-holomorphic vector bundle, and ξ a smooth (0,1)-form with coefficients in E.The main result of this article states that if ξ and the curvature of E are both Lnloc,then the equation ∂u = ξ has a smooth solution on a punctured neighbourhood of x0.Applications of this theorem to problems of holomorphic extension, and in particular a result of Kohn-Rossi type for sections over a CR-hypersurface, are discussed in the final section. |
|