Let
be an open
Riemann surface and
be an integer. We prove that on any closed discrete subset of
one can prescribe the values of a conformal minimal immersion
. Our
result also ensures jet-interpolation of given finite order, and hence, in particular, one
may in addition prescribe the values of the generalized Gauss map. Furthermore,
the interpolating immersions can be chosen to be complete, proper into
if the prescription of values is proper, and injective if
and
the prescription of values is injective. We may also prescribe the flux map of the
examples.
We also show analogous results for a large family of directed holomorphic immersions
,
including null curves.
Dedicated to Franc Forstnerič on the
occasion of his sixtieth birthday
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