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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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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.
A characterisation of the HoffmanWohlgemuth surfaces in terms of their symmetries
 J. Differential Geom
"... For an embedded singly periodic minimal surface ˜ M with genus ≥ 4 and annular ends, some weak symmetry hypotheses imply its congruence with one of the HoffmanWohlgemuth examples. We give a very geometrical proof of this fact, along which they come out many valuable clues for the understanding of ..."
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For an embedded singly periodic minimal surface ˜ M with genus ≥ 4 and annular ends, some weak symmetry hypotheses imply its congruence with one of the HoffmanWohlgemuth examples. We give a very geometrical proof of this fact, along which they come out many valuable clues for the understanding of these surfaces. 1.
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.
A CONSTRUCTION METHOD FOR TRIPLY PERIODIC MINIMAL SURFACES
"... Abstract. A uniform and elementary treatment of many classical and new embedded triply periodic minimal surfaces in Euclidean space, based on a SchwarzChristoffel formula for periodic polygons in the plane, is given. ..."
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Abstract. A uniform and elementary treatment of many classical and new embedded triply periodic minimal surfaces in Euclidean space, based on a SchwarzChristoffel formula for periodic polygons in the plane, is given.