Revista Matemática Iberoamericana


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Volume 31, Issue 4, 2015, pp. 1231–1262
DOI: 10.4171/RMI/867

Published online: 2015-12-23

Positive metric currents and holomorphic chains in Hilbert spaces

Samuele Mongodi[1]

(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