Revista Matemática Iberoamericana
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Published online: 2015-12-23
Positive metric currents and holomorphic chains in Hilbert spacesSamuele Mongodi (1) Università di Roma 'Tor Vergata', Italy
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.
Keywords: Positive currents, holomorphic chains, metric currents, complex Plateau problem
Mongodi Samuele: Positive metric currents and holomorphic chains in Hilbert spaces. Rev. Mat. Iberoam. 31 (2015), 1231-1262. doi: 10.4171/RMI/867