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24
Construction of Triply Periodic Minimal Surfaces
, 1996
"... We discuss the construction of triply period minimal surfaces. This includes concepts for constructing new examples as well as a discussion of numerical computations based on the new concept of discrete minimal surfaces. As a result we present a wealth of old and new examples and suggest directio ..."
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Cited by 10 (2 self)
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We discuss the construction of triply period minimal surfaces. This includes concepts for constructing new examples as well as a discussion of numerical computations based on the new concept of discrete minimal surfaces. As a result we present a wealth of old and new examples and suggest directions for further generalizations.
A FAMILY OF TRIPLY PERIODIC COSTA SURFACES
 PACIFIC JOURNAL OF MATHEMATICS
, 2003
"... We derive global Weierstrass representations for complete minimal surfaces obtained by substituting the ends of the Costa surface by symmetry curves. ..."
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Cited by 5 (1 self)
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We derive global Weierstrass representations for complete minimal surfaces obtained by substituting the ends of the Costa surface by symmetry curves.
Infinite periodic discrete minimal surfaces without selfintersections
 Balkan J. Geom. Appl
"... Abstract. A triangulated piecewiselinear minimal surface in Euclidean 3space R 3 defined using a variational characterization is critical for area amongst all continuous piecewiselinear variations with compact support that preserve the simplicial structure. We explicitly construct examples of suc ..."
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Cited by 3 (0 self)
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Abstract. A triangulated piecewiselinear minimal surface in Euclidean 3space R 3 defined using a variational characterization is critical for area amongst all continuous piecewiselinear variations with compact support that preserve the simplicial structure. We explicitly construct examples of such surfaces that are embedded and are periodic in three independent directions of R 3.
Triply periodic minimal surfaces bounded by vertical symmetry planes
 Manuscripta Math
"... This material is based upon work for the NSF under Award No.DMS 0139476. Abstract. We give a uniform and elementary treatment of many classical and new triply periodic minimal surfaces in Euclidean space, based on a SchwarzChristoffel formula for periodic polygons in the plane. Our surfaces share ..."
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Cited by 1 (1 self)
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This material is based upon work for the NSF under Award No.DMS 0139476. Abstract. We give a uniform and elementary treatment of many classical and new triply periodic minimal surfaces in Euclidean space, based on a SchwarzChristoffel formula for periodic polygons in the plane. Our surfaces share the property that vertical symmetry planes cut them into simply connected pieces. 2000 Mathematics Subject Classification. Primary 53A10; Secondary 49Q05, 53C42. Key words and phrases. Minimal surface, triply periodic, SchwarzChristoffel formula.
Description of cubic liquidcrystalline structures using simple surface foliations
 J. Chem. Soc. Faraday Trans
, 1994
"... ..."
Isoperimetric inequalities in crystallography, preprint
, 2003
"... The study of the isoperimetric problem in the presence of crystallographic symmetries is an interesting unsolved question in classical differential geometry: Given a space group G, we want to describe, among surfaces dividing Euclidean 3space into two Ginvariant regions with prescribed volume frac ..."
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Cited by 1 (0 self)
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The study of the isoperimetric problem in the presence of crystallographic symmetries is an interesting unsolved question in classical differential geometry: Given a space group G, we want to describe, among surfaces dividing Euclidean 3space into two Ginvariant regions with prescribed volume fractions, those which have
Scherk Saddle Towers of Genus Two in R 3
, 906
"... In 1996 M. Traizet obtained singly periodic minimal surfaces with Scherk ends of arbitrary genus by desingularizing a set of vertical planes at their intersections. However, in Traizet’s work it is not allowed that three or more planes intersect at the same line. In our paper, by a saddletower we c ..."
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In 1996 M. Traizet obtained singly periodic minimal surfaces with Scherk ends of arbitrary genus by desingularizing a set of vertical planes at their intersections. However, in Traizet’s work it is not allowed that three or more planes intersect at the same line. In our paper, by a saddletower we call the desingularization of such “forbidden ” planes into an embedded singly periodic minimal surface. We give explicit examples of genus two and discuss some advances regarding this problem. Moreover, our examples are the first ones containing Gaussian geodesics, and for the first time we prove embeddedness of the surfaces CSSCFF and CSSCCC from CallahanHoffmanMeeksWohlgemuth. 1.
TRIGONAL MINIMAL SURFACES IN FLAT TORI
, 2007
"... Abstract. In this paper, we study trigonal minimal surfaces in flat tori. First, we show a topological obstruction similar to that of hyperelliptic minimal surfaces. Actually, the genus of trigonal minimal surface in 3dimensional flat torus must be 1 (mod 3). Next, we construct an explicit example ..."
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Abstract. In this paper, we study trigonal minimal surfaces in flat tori. First, we show a topological obstruction similar to that of hyperelliptic minimal surfaces. Actually, the genus of trigonal minimal surface in 3dimensional flat torus must be 1 (mod 3). Next, we construct an explicit example in the higher codimensional case. This surface satisfies good properties and is theoretically distinct from traditional examples. 1.
TRIGONAL MINIMAL SURFACES IN FLAT TORI
, 2007
"... Abstract. In this paper, we study trigonal minimal surfaces in flat tori. First, we show a topological obstruction similar to that of hyperelliptic minimal surfaces. Actually, the genus of trigonal minimal surface in 3dimensional flat torus must be 1 (mod 3). Next, we construct an explicit example ..."
Abstract
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Abstract. In this paper, we study trigonal minimal surfaces in flat tori. First, we show a topological obstruction similar to that of hyperelliptic minimal surfaces. Actually, the genus of trigonal minimal surface in 3dimensional flat torus must be 1 (mod 3). Next, we construct an explicit example in the higher codimensional case. This surface satisfies good properties and is theoretically distinct from traditional examples. 1.