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math.CV2012
Application of metric currents to complex analysis
Samuele Mongodi
In 2000, Ambrosio and Kirchheim, with the paper "Currents in metric spaces", settled the foundations of a theory of currents on metric spaces and used it to pose and solve Plateau'…
math.AP2012★ 2 cited
A low rank property and nonexistence of higher dimensional horizontal Sobolev sets
Valentino Magnani, Jan Malý, Samuele Mongodi
We establish a "low rank property" for Sobolev mappings that pointwise solve a first order nonlinear system of PDEs, whose smooth solutions have the so-called "contact property". A…
math.CV2012
Positive metric currents and holomorphic chains in Hilbert spaces
Samuele Mongodi
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 t…