The exterior Plateau problem in higher codimension - Tomi, Friedrich; Jorge, Luquésio (Journal of mathematical sciences, 2008)
We prove existence theorems for two-dimensional, noncompact, complete minimal surfaces in ℝn of annular type, which span a given contour and have a finite total curvature end and prescribed asymptotical behavior. For arbitrary rectifiable Jordan curves, we show the existence of such surfaces with a flat end, i.e., within a bounded distance from a 2-plane. For more restricted classes of curves, we prove the existence of minimal surfaces with higher multiplicity flat ends as well as of surfaces with polynomial-type nonflat ends.
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