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Sur le prolongement des courants positifs fermés avec conditions sur les tranches. (Extending closed positive currents with conditions on slices). (French) Zbl 0762.32005

The authors’ abstract: “Let \(A\) be a compact, complete pluripolar subset in \(\Delta^{n-k}\) and let \(T\) be a positive \(d\)-closed current in \(\Delta^ k\times(\Delta^{n-k}\setminus A)\) of complex dimension \(k\) such that the slice \(\langle T,\pi,z'\rangle\) exists and has finite mass for every \(z'\) in a non pluripolar subset \(E\) of \(\Delta^ k\). We give sufficient conditions on \(T\), \(A\) and \(E\) to assert that the current has a closed positive extension across \(\Delta^ k\times A\)”.

MSC:

32C30 Integration on analytic sets and spaces, currents
32D15 Continuation of analytic objects in several complex variables
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