The exterior Plateau problem in higher codimension

• Verfasst von: Tomi, Friedrich [VerfasserIn]
• Verfasst von: Jorge, Luquésio [VerfasserIn]
• Titel: The exterior Plateau problem in higher codimension
• Verf.angabe: F. Tomi and L.P. Jorge
• E-Jahr: 2008
• Jahr: March 2008
• Umfang: 14 S.
• Teil: volume:149
• Teil: year:2008
• Teil: number:6
• Teil: pages:1741-1754
• Teil: extent:14
• Fussnoten: Gesehen am 15.06.2021
• Titel Quelle: Enthalten in: Journal of mathematical sciences
• Ort Quelle: New York, NY : Consultants Bureau, 1973
• Jahr Quelle: 2008
• Band/Heft Quelle: 149(2008), 6, Seite 1741-1754
• ISSN Quelle: 1573-8795
• DOI: doi:10.1007/s10958-008-0093-1
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 176049495X

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.