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Positive metric currents and holomorphic chains in Hilbert spaces. (English) Zbl 1332.32015
Summary: We present some results concerning currents of integration on finite-dimensional analytic spaces in Hilbert spaces, using the setting of metric currents. In particular, we obtain the characterization of such currents as positive closed \((k,k)\)-integer rectifiable currents and solve the boundary problem for holomorphic chains.

MSC:
32C30 Integration on analytic sets and spaces, currents
32V25 Extension of functions and other analytic objects from CR manifolds
46G20 Infinite-dimensional holomorphy
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