The graphs of smooth functions are dense in the space of Cartesian currents on a smooth bounded domain, but not every Cartesian current is the limit of such graphs

Research Report MRR98-045

The graphs of smooth functions are dense in the space of Cartesian currents on a smooth bounded domain, but not every Cartesian current is the limit of such graphs

Alex Coventry

Abstract: In [3], Giaquinta et al wrote that it seems reasonable to conjecture that the cartesian currents given by graphs of smooth functions are dense in the space of cartesian currents. This paper proves that this is the case for smooth bounded domains. An example is also given of a cartesian current which is not the weak limit of any sequence of currents given by graphs of smooth functions. This resolves an implicit question raised in [4, page 1].

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