On the nonexistence of boundary branch points for minimal surfaces spanning smooth contours II

2011 ◽  
Vol 10 (2) ◽  
pp. 253-277
Author(s):  
A. J. Tromba
Keyword(s):  
Minimal Surfaces ◽  
Branch Points

Minimal surfaces with self-intersections along straight lines. I. Derivation and properties

1999 ◽  
Vol 55 (1) ◽  
pp. 58-64 ◽  
Author(s):  
E. Koch ◽  
W. Fischer
Keyword(s):  
Minimal Surface ◽  
Symmetry Group ◽  
Minimal Surfaces ◽  
Special Kind ◽  
Branch Points ◽  
Euler Characteristics ◽  
Oriented Surface ◽  
Periodic Minimal Surface ◽  
Full Symmetry ◽  
Straight Lines

A special kind of three-periodic minimal surface has been studied, namely surfaces that are generated from disc-like-spanned skew polygons and that intersect themselves exclusively along straight lines. A new procedure for their derivation is introduced in this paper. Several properties of each such surface may be deduced from its generating polygon: the full symmetry group of the surface, its orientability, the symmetry group of the oriented surface, the pattern of self-intersections, the branch points of the surface, the symmetry and periodicity of the spatial subunits demarcated by the surface, and the Euler characteristics both of the surface and of the spatial subunits. The corresponding procedures are described and illustrated by examples.

Polar varieties and bipolar surfaces of minimal surfaces in the n-sphere

2021 ◽  
Author(s):  
Katsuhiro Moriya
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Minimal Immersion ◽  
The Other ◽  
Branch Points

AbstractFor a given minimal surface in the n-sphere, two ways to construct a minimal surface in the m-sphere are given. One way constructs a minimal immersion. The other way constructs a minimal immersion which may have branch points. The branch points occur exactly at each point where the original minimal surface is geodesic. If a minimal surface in the 3-sphere is given, then these ways construct Lawson’s polar variety and bipolar surface.

On interior branch points of minimal surfaces

1980 ◽  
Vol 171 (2) ◽  
pp. 133-154 ◽  
Author(s):  
Michael Beeson
Keyword(s):  
Minimal Surfaces ◽  
Branch Points ◽  
Interior Branch

Exclusion of boundary branch points for minimal surfaces

Analysis ◽  
2011 ◽  
Vol 31 (2) ◽  
Author(s):  
Matthias Bergner ◽  
Ruben Jakob
Keyword(s):  
Minimal Surfaces ◽  
Branch Points
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