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- Title
The exterior Plateau problem in higher codimension.
- Authors
Tomi, F.; Jorge, L. P.
- Abstract
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.
- Subjects
EXISTENCE theorems; MINIMAL surfaces; MAXIMA &; minima; PLATEAU'S problem; CURVES on surfaces
- Publication
Journal of Mathematical Sciences, 2008, Vol 149, Issue 6, p1741
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-008-0093-1