The exterior Plateau problem in higher codimension
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...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
March 2008
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| In: |
Journal of mathematical sciences
Year: 2008, Volume: 149, Issue: 6, Pages: 1741-1754 |
| ISSN: | 1573-8795 |
| DOI: | 10.1007/s10958-008-0093-1 |
| Online Access: | Resolving-System, lizenzpflichtig, Volltext: https://doi.org/10.1007/s10958-008-0093-1 Verlag, lizenzpflichtig, Volltext: https://link.springer.com/article/10.1007/s10958-008-0093-1 
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| Author Notes: | F. Tomi and L.P. Jorge |
| Summary: | 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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| Item Description: | Gesehen am 15.06.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1573-8795 |
| DOI: | 10.1007/s10958-008-0093-1 |