On embeddedness of area-minimizing disks, and an application to constructing complete minimal surfaces
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چکیده
منابع مشابه
On Embeddedness of Area-Minimizing Disks, and an Application to Constructing Complete Minimal Surfaces
Let α be a polygonal Jordan curve in R 3 . We show that if α satisfies certain conditions, then the least-area Douglas-Radó disk in R 3 with boundary α is unique and is a smooth graph. As our conditions on α are not included amongst previously known conditions for embeddedness, we are enlarging the set of Jordan curves in R 3 which are known to be spanned by an embedded least-area disk. As an a...
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15 صفحه اولEmbeddedness of Minimal Surfaces with Total Boundary Curvature at Most
This paper proves that classical minimal surfaces of arbitrary topological type with total boundary curvature at most 4 must be smoothly embedded. Related results are proved for varifolds and for soap lm surfaces. In a celebrated paper N3] of 1973, Nitsche proved that if ? is an analytic simple closed curve in R 3 with total curvature at most 4, then ? bounds exactly one minimal disk M. Further...
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SuÆcient conditions for which a minimal graph over a nonconvex domain is area-minimizing are presented. The conditions are shown to hold for subsurfaces of Enneper's surface, the singly periodic Scherk surface, and the associated surfaces of the doubly periodic Scherk surface which previously were unknown to be area-minimizing. In particular these surfaces are graphs over (angularly accessible)...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2000
ISSN: 0025-5645
DOI: 10.2969/jmsj/05210025