A method to exclude branch points of minimal surfaces

Daniel Wienholtz

doi:10.1007/s005260050107

A method to exclude branch points of minimal surfaces

Calculus of Variations and Partial Differential Equations ◽

10.1007/s005260050107 ◽

1998 ◽

Vol 7 (3) ◽

pp. 219-247 ◽

Cited By ~ 2

Author(s):

Daniel Wienholtz

Keyword(s):

Minimal Surfaces ◽

Branch Points

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

Acta Crystallographica Section A Foundations of Crystallography ◽

10.1107/s0108767398007521 ◽

1999 ◽

Vol 55 (1) ◽

pp. 58-64 ◽

Cited By ~ 5

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.

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

Annals of Global Analysis and Geometry ◽

10.1007/s10455-021-09793-2 ◽

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.

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