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Let X be a connected normal complex space of dimension n>=2 which is(n-1)-complete, and let p: M -> X be a resolution of singularities. By use ofTakegoshi's generalization of the Grauert-Riemenschneider vanishing theorem, wededuce H^1_{cpt}(M,O)=0, which in turn implies Hartogs' extension theorem on Xby the d-bar-technique of Ehrenpreis.

A d-bar-theoretical proof of Hartogs' extension theorem on (n-1)-complete spaces